Rational Points on Varieties

[1]  T. Ekedahl Canonical models of surfaces of general type in positive characteristic , 1988 .

[2]  J. Tate,et al.  $WC$-groups over $p$-adic fields , 1958 .

[3]  S. Mori Threefolds whose canonical bundles are not numerically effective. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[4]  James S. Milne,et al.  Class Field Theory , 2013 .

[5]  M. Raynaud Anneaux locaux henséliens , 1970 .

[6]  Nicholas M. Katz,et al.  An overview of Deligne''s proof of the Riemann hypothesis for varieties over finite fields , 1976 .

[7]  加藤 和也 A generalization of local class field theory by using K-groups I, II, III = K-群による局所類体論の一般化 , 1980 .

[8]  Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups , 1990 .

[9]  F. Campana Special Varieties and classification Theory , 2001, math/0110051.

[10]  M. Artin Algebraic construction of Brieskorn's resolutions , 1974 .

[11]  C. Chevalley On algebraic group varieties. , 1954 .

[12]  David Harari,et al.  Groupes algébriques et points rationnels , 2002 .

[13]  M. Handzic 5 , 1824, The Banality of Heidegger.

[14]  M. Kneser Galois-Kohomologie halbeinfacher algebraischer Gruppen überp-adischen Körpern. I , 1965 .

[15]  C. Simpson Local Systems on Proper Algebraic V -manifolds , 2010, 1010.3363.

[16]  D. Toledo Projective varieties with non-residually finite fundamental group , 1993 .

[17]  B. Poonen The Hasse Principle for Complete Intersections in Projective Space , 2001 .

[18]  Sivaramakrishna Anantharaman Schémas en groupes, espaces homogènes et espaces algébriques sur une base de dimension 1 , 1973 .

[19]  Y. I. Manin LE GROUPE DE BRAUER-GROTHENDIECK EN GÉOMÉTRIE DIOPHANTIENNE , 1996 .

[20]  Ju. Manin,et al.  RATIONAL SURFACES OVER PERFECT FIELDS. II , 1967 .

[21]  Jean Dieudonne,et al.  Fondements de la géométrie algébrique moderne , 1969 .

[22]  B. Segre A Note on Arithmetical Properties of Cubic Surfaces , 1943 .

[23]  J. Tits,et al.  Groupes algébriques sur un corps local: III. Compléments et applications à la cohomologie galoisienne , 1987 .

[24]  Alexander Grothendieck,et al.  Technique de descente et théorèmes d'existence en géométrie algébrique. VI. Les schémas de Picard : propriétés générales , 1962 .

[25]  P. Roquette Isomorphisms of generic splitting fields of simple algebras. , 1964 .

[26]  H. Esnault Coniveau over $p$-adic fields and points over finite fields , 2007, 0704.1273.

[27]  E. Victor Flynn,et al.  Coverings of Curves of Genus 2 , 2000, ANTS.

[28]  Jean-Pierre Serre,et al.  Local Class Field Theory , 1979 .

[29]  Wilhelm Schlag,et al.  A Course in Complex Analysis and Riemann Surfaces , 2014 .

[30]  M. Raynaud Faisceaux amples sur les schémas en groupes et les espaces homogènes , 1970 .

[31]  J. Tate,et al.  Algebraic cycles and poles of zeta functions , 1965 .

[32]  J. Neukirch,et al.  Cohomology of number fields , 2000 .

[33]  D. Mumford The red book of varieties and schemes , 1988 .

[34]  D. Gieseker Global moduli for surfaces of general type , 1977 .

[35]  M. Artin On the joins of hensel rings , 1971 .

[36]  P. Russell Forms of the affine line and its additive group , 1970 .

[37]  H. Hironaka Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II , 1964 .

[38]  Megumu Miwa On Mordell's conjecture for the curve over function field with arbitrary constant field , 1969 .

[39]  A. Weil,et al.  Variétés abéliennes et courbes algébriques , 1948 .

[40]  Amanda Knecht,et al.  Degree of Unirationality for del Pezzo Surfaces over Finite Fields , 2013, 1307.3215.

[41]  B. Poonen Insufficiency of the Brauer-Manin obstruction applied to étale covers , 2008, 0806.1312.

[42]  B. Poonen Why All Rings Should Have a 1 , 2014, Mathematics Magazine.

[43]  J. Stix,et al.  Field Arithmetic , 2019, Oberwolfach Reports.

[44]  J. Neukirch Algebraic Number Theory , 1999 .

[45]  J. Tate Genus change in inseparable extensions of function fields , 1952 .

[46]  J. Colliot-Thélène The Hasse principle in a pencil of algebraic varieties , 1998 .

[47]  N. Koblitz p-adic Numbers, p-adic Analysis, and Zeta-Functions , 1977 .

[48]  Rational points in henselian discrete valuation rings , 1966 .

[49]  J. Tate,et al.  DUALITY THEOREMS IN GALOIS COHOMOLOGY OVER NUMBER FIELDS , 2010 .

[50]  Robert Steinberg,et al.  Regular elements of semisimple algebraic groups , 1965 .

[51]  Alexander Grothendieck,et al.  Formule de Lefschetz et rationalité des fonctions $L$ , 1966 .

[52]  V. Platonov The Problem of Strong Approximation and the Kneser - Tits Conjecture , 1969 .

[53]  A. Borel,et al.  Théorèmes de finitude en cohomologie galoisienne , 1964 .

[54]  H'elene Esnault,et al.  Varieties over a finite field with trivial Chow group of 0-cycles have a rational point , 2002, math/0207022.

[55]  P. Salberger Some New Hasse Principles For Conic Bundle Surfaces , 1990 .

[56]  Sadao Saito,et al.  Global class field theory of arithmetic schemes , 1986 .

[57]  J. Colliot-Thélène,et al.  SURFACES DE DEL PEZZO SANS POINT RATIONNEL SUR UN CORPS DE DIMENSION COHOMOLOGIQUE UN , 2003, Journal of the Institute of Mathematics of Jussieu.

[58]  D. Lewis Cubic Homogeneous Polynomials Over -Adic Number Fields , 1952 .

[59]  J. Kollár,et al.  Rational connectedness and bound-edness of Fano manifolds , 1992 .

[60]  G. Margulis Cobounded subgroups of algebraic groups over local fields , 1977 .

[61]  Brendan Hassett,et al.  Rational surfaces over nonclosed fields , 2009 .

[62]  H. Hochstadt Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable; 3rd ed. (Lars V. Ahlfors) , 1980 .

[63]  A. Weil Numbers of solutions of equations in finite fields , 1949 .

[64]  Kindra M Kelly-Scumpia,et al.  51 , 2015, Tao te Ching.

[65]  飯高 茂 Algebraic geometry : an introduction to birational geometry of algebraic varieties , 1982 .

[66]  J. Colliot-Thélène,et al.  Variétés unirationnelles non rationnelles: au-delà de l'exemple d'Artin et Mumford , 1989 .

[67]  V. Voskresenskii ON TWO-DIMENSIONAL ALGEBRAIC TORI. II , 1967 .

[68]  G. Harder Halbeinfache Gruppenschemata über Dedekindringen , 1967 .

[69]  Joseph H. Silverman,et al.  The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[70]  A. J. Jong A result of Gabber by , 2005 .

[71]  Herrn Chevalley,et al.  Bemerkung zur vorstehenden Arbeit , 1935 .

[72]  P. Sarnak,et al.  Some hypersurfaces in P4 and the Hasse-principle , 1995 .

[73]  Jean-Pierre Serre Géométrie algébrique et géométrie analytique , 1956 .

[74]  J. Oesterlé Nombres de Tamagawa et groupes unipotents en caractéristique p , 1984 .

[75]  A. Grothendieck Le groupe de Brauer : I. Algèbres d'Azumaya et interprétations diverses , 1966 .

[76]  A. Grothendieck Seminaire de geometrie algebrique 1960-61 , 1961 .

[77]  B. Poonen THE METHOD OF CHABAUTY AND COLEMAN WILLIAM MCCALLUM AND , 2017 .

[78]  Tonny A. Springer Linear Algebraic Groups , 1981 .

[79]  J. Koenigsmann Undecidability in Number Theory , 2013, 1309.0441.

[80]  K. Fujiwara A Proof of the Absolute Purity Conjecture (after Gabber) , 2002 .

[81]  A. Meyers Reading , 1999, Language Teaching.

[82]  Craig Huneke,et al.  Commutative Algebra I , 2012 .

[83]  Joe Harris,et al.  Moduli of curves , 1998 .

[84]  W. Waterhouse,et al.  Introduction to Affine Group Schemes , 1979 .

[85]  M. Brion Anti-affine algebraic groups , 2007, 0710.5211.

[86]  T. Chinburg Minimal Models for Curves over Dedekind Rings , 1986 .

[87]  Kevin R. Coombes,et al.  Every rational surface is separably split , 1988 .

[88]  M. Stoll Finite descent obstructions and rational points on curves , 2006, math/0606465.

[89]  A. Borel,et al.  Algebraic groups and discontinuous subgroups , 1966 .

[90]  Séminaire Bourbaki,et al.  Dix exposés sur la cohomologie des schémas , 1968 .

[91]  Stephen S. Shatz,et al.  Profinite Groups, Arithmetic, and Geometry. , 1972 .

[92]  James Ax,et al.  ZEROES OF POLYNOMIALS OVER FINITE FIELDS. , 1964 .

[93]  J. Bulthuis Rational points on del Pezzo surfaces of degree one , 2018 .

[94]  David Harari Méthode des fibrations et obstruction de Manin , 1994 .

[95]  H. Swinnerton-Dyer,et al.  The Hasse problem for rational surfaces. , 1975 .

[96]  W. Chow On the Projective Embedding of Homogeneous Varieties , 1957 .

[97]  Andreas-Stephan Elsenhans,et al.  The Diophantine Equation x4 + 2 y4 = z4 + 4 w4 , 2006, Math. Comput..

[98]  Marvin J. Greenberg Lectures on Forms in Many Variables , 2018 .

[99]  Bjorn Poonen,et al.  COMPUTING RATIONAL POINTS ON CURVES , 2001 .

[100]  Y. Tschinkel,et al.  Effectivity of Brauer–Manin obstructions on surfaces , 2010, 1005.4331.

[101]  Kazuya Kato,et al.  On the conjectures of Birch and Swinnerton-Dyer in characteristic p>0 , 2003 .

[102]  J. Voloch Diophantine geometry in characteristic p: a survey , 2013 .

[103]  C. Weibel,et al.  AN INTRODUCTION TO HOMOLOGICAL ALGEBRA , 1996 .

[104]  P. Scholze,et al.  The pro-\'etale topology for schemes , 2013, 1309.1198.

[105]  G. Horrocks ETALE COHOMOLOGY AND THE WEIL CONJECTURE (Ergebnisse der Mathematik und ihrer Grenzgebiete 3 (13)) , 1991 .

[106]  F. Campana Orbifolds, special varieties and classification theory , 2004 .

[107]  J. Neu Singular Perturbation in the Physical Sciences , 2015 .

[108]  Carlos R. Videla Hilbert’s tenth problem for rational function fields in characteristic 2 , 1994 .

[109]  B. Hodson,et al.  The effect of passage in vitro and in vivo on the properties of murine fibrosarcomas. II. Sensitivity to cell-mediated cytotoxicity in vitro. , 1985, British Journal of Cancer.

[110]  Y. Matsumoto Good reduction criterion for K3 surfaces , 2014, 1401.1261.

[111]  Colin Clarke Benjamin , 2013, Tempo.

[112]  J. Tate,et al.  On the conjectures of Birch and Swinnerton-Dyer and a geometric analog , 1966 .

[113]  André Weil,et al.  Abstract versus classical algebraic geometry , 1979 .

[114]  Yuri Tschinkel,et al.  Effectivity of Brauer–Manin obstructions☆ , 2006 .

[115]  Y. Manin RATIONAL POINTS ON ALGEBRAIC CURVES , 1964 .

[116]  C. Demarche Obstruction de descente et obstruction de Brauer–Manin étale , 2009 .

[117]  A. Grothendieck Étude locale des schémas et des morphismes de schémas , 1964 .

[118]  G. Ballew,et al.  The Arithmetic of Elliptic Curves , 2020, Elliptic Curves.

[119]  A. Skorobogatov On a theorem of Enriques - Swinnerton-Dyer , 1993 .

[120]  J. Coates,et al.  The Conjecture of Birch and Swinnerton-Dyer , 1977, Open Problems in Mathematics.

[121]  G. Harder Über die Galoiskohomologie halbeinfacher algebraischer Gruppen. III. , 1975 .

[122]  P. Griffiths,et al.  The intermediate Jacobian of the cubic threefold , 1972 .

[123]  G. Faltings Endlichkeitssätze für abelsche Varietäten über Zahlkörpern , 1983 .

[124]  Gregory H. Moore The emergence of open sets, closed sets, and limit points in analysis and topology , 2008 .

[125]  A. Weil Sur les courbes algébriques et les variétés qui s'en déduisent , 1948 .

[126]  Alexander Grothendieck,et al.  Éléments de géométrie algébrique : II. Étude globale élémentaire de quelques classes de morphismes , 1961 .

[127]  H. Swinnerton-Dyer,et al.  Notes on elliptic curves. II. , 1963 .

[128]  M. Artin Lipman’s Proof of Resolution of Singularities for Surfaces , 1986 .

[129]  Emmanuel Peyre Points de hauteur bornée et géométrie des variétés , 2001 .

[130]  I︠u︡. I. Manin,et al.  Cubic forms; algebra, geometry, arithmetic , 1974 .

[131]  David Harari Weak Approximation on Algebraic Varieties , 2004 .

[132]  Nicholas M. Katz,et al.  Sums of Betti Numbers in Arbitrary Characteristic , 2001 .

[133]  Qing Liu,et al.  Algebraic Geometry and Arithmetic Curves , 2002 .

[134]  F. Campana,et al.  Connexité rationnelle des variétés de Fano , 1992 .

[135]  Maurice Auslander,et al.  The Brauer group of a commutative ring , 1960 .

[136]  J. Milne Comparison of the Brauer group with the Tate-Safarevic group , 1982 .

[137]  Franz W. Peren Arithmetic , 1903, Nature.

[138]  Zinovy Reichstein,et al.  Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties , 1999, Canadian Journal of Mathematics.

[139]  B. Fantechi Fundamental Algebraic Geometry , 2005 .

[140]  S. Kochen,et al.  Diophantine Problems Over Local Fields I , 1965 .

[141]  B. Conrad MINIMAL MODELS FOR ELLIPTIC CURVES , 2003 .

[142]  Ronald van Luijk,et al.  Unirationality of del Pezzo surfaces of degree 2 over finite fields , 2014, 1505.01145.

[143]  D. Saltman The Brauer group and the center of generic matrices , 1985 .

[144]  G I Arhipov,et al.  ON LOCAL REPRESENTATION OF ZERO BY A FORM , 1982 .

[145]  János Kollár,et al.  Lectures on resolution of singularities , 2007 .

[146]  Paul Vojta Siegel's theorem in the compact case , 1991 .

[147]  David Harari Flèches de spécialisations en cohomologie étale et applications arithmétiques , 1997 .

[148]  A. Borel,et al.  Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups , 1989 .

[149]  M. Mella,et al.  Quadratic families of elliptic curves and unirationality of degree 1 conic bundles , 2014, 1412.3673.

[150]  F. Murnaghan,et al.  LINEAR ALGEBRAIC GROUPS , 2005 .

[151]  B. Conrad Finiteness theorems for algebraic groups over function fields , 2011, Compositio Mathematica.

[152]  M. Artin,et al.  Some Elementary Examples of Unirational Varieties Which are Not Rational , 1972 .

[153]  W. Waterhouse Basically bounded functors and flat sheaves. , 1975 .

[154]  W. Bauer On the conjecture of Birch and Swinnerton-Dyer for abelian varieties over function fields in characteristicp>0 , 1992 .

[155]  H. Grauert Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper , 1965 .

[156]  S. Lang Higher dimensional diophantine problems , 1974 .

[157]  E. Bombieri Canonical models of surfaces of general type , 1973 .

[158]  Eberhard Freitag,et al.  Etale Cohomology and the Weil Conjecture , 1988 .

[159]  Akhil Mathew,et al.  The p-adic Numbers , 2009 .

[160]  J. Sansuc,et al.  Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres. , 1981 .

[161]  J. Bertin,et al.  Propriétés générales des schémas en groupes , 1970 .

[162]  J. Igusa ON SOME PROBLEMS IN ABSTRACT ALGEBRAIC GEOMETRY. , 1955, Proceedings of the National Academy of Sciences of the United States of America.

[163]  Marta Pieropan On the unirationality of Del Pezzo surfaces over an arbitrary field , 2012 .

[164]  Friedrich Karl Schmidt,et al.  Analytische Zahlentheorie in Körpern der Charakteristik p , 1931 .

[165]  Yongqi Liang Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus de l'espace projectif , 2014 .

[166]  B. Poonen,et al.  Random Diophantine Equations , 2004 .

[167]  J. Voloch A Diophantine problem on algebraic curves over function fields of positive characteristic , 1991 .

[168]  Joseph H. Silverman,et al.  Diophantine Geometry: An Introduction , 2000, The Mathematical Gazette.

[169]  Jean-Pierre Serre Morphismes universels et variété d'Albanese , 1959 .

[170]  J. Voloch On the conjectures of Mordell and Lang in positive characteristics , 1991 .

[171]  A. Skorobogatov,et al.  Weak approximation for surfaces defined by two quadratic forms , 1991 .

[172]  Olivier Wittenberg,et al.  On the fibration method for zero-cycles and rational points , 2014, 1409.0993.

[173]  A. Skorobogatov Descent obstruction is equivalent to étale Brauer–Manin obstruction , 2009 .

[174]  Shigefumi Mori,et al.  Threefolds Whose Canonical Bundles Are Not Numerically Effective (Recent Topics in Algebraic Geometry) , 1980 .

[175]  D. Mumford,et al.  The irreducibility of the space of curves of given genus , 1969 .

[176]  M. Artin SOME NUMERICAL CRITERIA FOR CONTRACTABILITY OF CURVES ON ALGEBRAIC SURFACES. , 1962 .

[177]  Gerd Faltings,et al.  Diophantine approximation on abelian varieties , 1991 .

[178]  Barry Mazur,et al.  The Topology of Rational Points , 1992, Exp. Math..

[179]  J. Kollár A conjecture of Ax and degenerations of Fano varieties , 2005, math/0512375.

[180]  P. Schneider Zur Vermutung von Birch und Swinnerton-Dyer über globalen Funktionenkörpern , 1982 .

[181]  Philippe Gille,et al.  Central Simple Algebras and Galois Cohomology , 2017 .

[182]  Beyond the Manin obstruction , 1997, alg-geom/9711006.

[183]  Ju. Manin,et al.  Rational surfaces over perfect fields , 1966 .

[184]  J. Cassels,et al.  On the Hasse principle for cubic surfaces , 1966 .

[185]  J. Serre,et al.  Sure la topologie des variétés algébriques en caractéristique p , 2003 .

[186]  Martin Cloutier,et al.  AVEC LA COLLABORATION DE , 2006 .

[187]  David Harari Weak approximation and non-abelian fundamental groups , 2000 .

[188]  V A Iskovskih,et al.  Minimal Models of Rational Surfaces Over Arbitrary Fields , 1980 .

[189]  Johan P. Hansen,et al.  INTERSECTION THEORY , 2011 .

[190]  A. Pianzola,et al.  Isotriviality and étale cohomology of Laurent polynomial rings , 2008 .

[191]  Kazuya Kato A generalization of local class field theory by using $K$-groups, II , 1977 .

[192]  Joseph Lipman,et al.  Desingularization of two-dimensional schemes , 1978 .

[193]  H. Hasse Darstellbarkeit von Zahlen durch quadratische Formen in einem beliebigen algebraischen Zahlkörper. , 1924 .

[194]  S. Lang On Quasi Algebraic Closure , 1952 .

[195]  J. Koll'ar Severi-Brauer varieties; a geometric treatment , 2016, 1606.04368.

[196]  Alexandra Shlapentokh HILBERT'S TENTH PROBLEM FOR RINGS OF ALGEBRAIC FUNCTIONS IN ONE VARIABLE OVER FIELDS OF CONSTANTS OF POSITIVE CHARACTERISTIC , 1992 .

[197]  G. Higman,et al.  A Finitely Generated Infinite Simple Group , 1951 .

[198]  Inta Bertuccioni Brauer groups and cohomology , 2005 .

[199]  János Kollár,et al.  Rational curves on algebraic varieties , 1995, Ergebnisse der Mathematik und ihrer Grenzgebiete.

[200]  M. Miyanishi,et al.  Unipotent algebraic groups , 1974 .

[201]  Vladimir Voevodsky,et al.  An exact sequence for $K_\ast^M/2$ with applications to quadratic forms , 2001, math/0101023.

[202]  Anthony Várilly-Alvarado Weak approximation on del Pezzo surfaces of degree 1 , 2008, 0801.2430.

[203]  Dino J. Lorenzini,et al.  On the Brauer group of a surface , 2005 .

[204]  D. Mumford Abelian Varieties Tata Institute of Fundamental Research , 1970 .

[205]  Emil Artin,et al.  Class Field Theory , 2008 .

[206]  F. Enriquès,et al.  Sulle irrazionalità da cui può farsi dipendere la risoluzione d'un' equazione algebricaf(xyz)=0 con funzioni razionali di due parametri , 1897 .

[207]  Bjorn Poonen Heuristics for the Brauer–Manin Obstruction for Curves , 2006, Exp. Math..

[208]  Brian Conrad,et al.  A MODERN PROOF OF CHEVALLEY’S THEOREM ON ALGEBRAIC GROUPS , 2004 .

[209]  S. Lang,et al.  NUMBER OF POINTS OF VARIETIES IN FINITE FIELDS. , 1954 .

[210]  Michael Francis Atiyah,et al.  Introduction to commutative algebra , 1969 .

[211]  On Albanese torsors and the elementary obstruction , 2006, math/0611284.

[212]  Yismaw Alemu,et al.  On zeros of forms over local fields , 1985 .

[213]  Bernard Dwork,et al.  On the Rationality of the Zeta Function of an Algebraic Variety , 1960 .

[214]  David Mumford,et al.  Stability of projective varieties , 1977 .

[215]  Jean-Louis Colliot-Thélène,et al.  Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties. , 1994 .

[216]  B. Conrad Weil and Grothendieck approaches to adelic points , 2012 .

[217]  Günter Tamme Introduction to étale cohomology , 1994 .

[218]  O. Gabber,et al.  On space filling curves and Albanese varieties , 2001 .

[219]  A. Grothendieck Technique de descente et théorèmes d'existence en géométrie algébrique. I. Généralités. Descente par morphismes fidèlement plats , 1960 .

[220]  Gorô Azumaya,et al.  On Maximally Central Algebras , 1951, Nagoya Mathematical Journal.

[221]  S. Lichtenbaum Curves Over Discrete Valuation Rings , 1968 .

[222]  J. Milne On the arithmetic of abelian varieties , 1972 .

[223]  Marvin J. Greenberg Rational points in henselian discrete valuation rings , 1966 .

[224]  A. Pfister Quadratic forms with applications to algebraic geometry and topology , 1995 .

[225]  C. Chevalley,et al.  Démonstration d’une hypothèse de M. Artin , 1935 .

[226]  J. Milne On a conjecture of Artin and Tate , 1975 .

[227]  P. Deligne La conjecture de Weil. I , 1974 .

[228]  Paul Monsky,et al.  On the automorphisms of hypersurfaces , 1963 .

[229]  C. Chevalley Un théorème d’arithmétique sur les courbes algébriques , 1979 .

[230]  B. Segre Variazione continua ed omotopia in geometria algebrica , 1960 .

[231]  Qing Liu,et al.  Néron models of algebraic curves , 2013, 1312.4822.

[232]  A. Grothendieck Exemples et Complements , 1971 .

[233]  Gopal Prasad,et al.  Strong approximation for semi-simple groups over function fields , 1977 .

[234]  Andrei S. Rapinchuk,et al.  Algebraic groups and number theory , 1992 .

[235]  B. Conrad Several approaches to non-archimedean geometry , 2008 .

[236]  S. Lang Some Applications of the Local Uniformization Theorem , 1954 .

[237]  N. Jacobson,et al.  Basic Algebra I , 1976 .

[238]  A. Grothendieck,et al.  Théorie des Topos et Cohomologie Etale des Schémas , 1972 .

[239]  J. Lipman Rational singularities, with applications to algebraic surfaces and unique factorization , 1969 .

[240]  Helmut Hasse,et al.  Number Theory , 2020, An Introduction to Probabilistic Number Theory.

[241]  S. A. Amitsur GENERIC SPLITTING FIELDS OF CENTRAL SIMPLE ALGEBRAS , 1955 .

[242]  S. Lang Complex Analysis , 1977 .

[243]  Martin Olsson,et al.  Algebraic Spaces and Stacks , 2016 .

[244]  Ju. Manin,et al.  THREE-DIMENSIONAL QUARTICS AND COUNTEREXAMPLES TO THE LÜROTH PROBLEM , 1971 .

[245]  C. Voisin,et al.  Cohomologie non ramifiée et conjecture de Hodge entière , 2010, 1005.2778.

[246]  Hilbert’s tenth problem for algebraic function fields of characteristic 2 , 2002, math/0207029.

[247]  A. Grothendieck,et al.  Éléments de géométrie algébrique , 1960 .

[248]  W. L. Baily,et al.  Enriques ' Classification of Surfaces in Char . p , II , 2005 .

[249]  R. Valenza,et al.  Fourier Analysis on Number Fields , 1998 .

[250]  N. Shepherd-barron,et al.  The Rationality of Quintic Del Pezzo Surfaces—A Short Proof , 1992 .

[251]  A. Skorobogatov,et al.  Non-abelian Cohomology and Rational Points , 2002, Compositio Mathematica.

[252]  M. Kneser Galois-Kohomologie halbeinfacher algebraischer Gruppen über p-adischen Körpern. II , 1965 .

[253]  M. Artin ON ISOLATED RATIONAL SINGULARITIES OF SURFACES. , 1966 .

[254]  J. Cremona Algorithms for Modular Elliptic Curves , 1992 .

[255]  A. Skorobogatov,et al.  Pathologies of the Brauer–Manin obstruction , 2013, 1310.5055.

[256]  Alexei N. Skorobogatov,et al.  Torsors and Rational Points , 2001 .

[257]  O. Gabber,et al.  Pseudo-reductive Groups , 2010 .

[258]  A. J. Jong,et al.  Smoothness, semi-stability and alterations , 1996 .

[259]  Y. Tschinkel,et al.  Stable rationality of quadric surface bundles over surfaces , 2016, 1603.09262.

[260]  Thanases Pheidas,et al.  Hilbert's Tenth Problem for fields of rational functions over finite fields , 1991 .

[261]  Pierre Samuel,et al.  Compléments a un article de Hans Grauert sur la conjecture de Mordell , 1966 .

[262]  Yang Cao Sous-groupe de Brauer invariant et obstruction de descente itérée , 2017, Algebra & Number Theory.

[263]  Tam'as Szamuely Galois groups and fundamental groups , 2009 .

[264]  János Kollár,et al.  Rationally Connected Varieties , 1996 .

[265]  S. Lang,et al.  Algebraic Groups Over Finite Fields , 1956 .

[266]  Jean-Pierre Serre,et al.  Lectures On The Mordell-Weil Theorem , 1989 .