Rational Points on Varieties
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[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 .