On Logarithmic Hodge-Witt Cohomology of Regular Schemes

In this paper, we prove the purity of the logarithmic Hodge-Witt cohomology for an excellent regular pair of characteristic p> 0 and the Gersten-type conjecture for the p-primary part of the Kato complex (the arithmetic Bloch-Ogus complex) of the spectrum of an excellent regular local ring of characteristic p> 0. They are generalizations of results of Gros and Suwa to regular schemes which are not necessarily smooth over a perfect field.

[1]  S. Saito,et al.  Kato homology of arithmetic schemes and higher class field theory over local fields. , 2003 .

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

[3]  B. Conrad.  Grothendieck Duality and Base Change , 2001 .

[4]  I. Panin.  THE EQUI-CHARACTERISTIC CASE OF THE GERSTEN CONJECTURE , 2000 .

[5]  K. Fujiwara.  Theory of tubular neighborhood in etale topology , 1995 .

[6]  Noriyuki Suwa.  A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves , 1995 .

[7]  T. Ogoma.  General Néron Desingularization Based on the Idea of Popescu , 1994 .

[8]  S. Saito.  COHOMOLOGICAL HASSE PRINCIPLE FOR A THREEFOLD OVER A FINITE FIELD , 1993 .

[9]  J. Colliot-Thélène.  On the Reciprocity Sequence in the Higher Class Field Theory of Function Fields , 1993 .

[10]  D. Popescu.  Letter to the editor: General Néron desingularization and approximation , 1990, Nagoya Mathematical Journal.

[11]  M. Gros,et al.  La conjecture de Gersten pour les faisceaux de Hodge-Witt logarithmique , 1988 .

[12]  D. Kirby,et al.  COMMUTATIVE RING THEORY (Cambridge Studies in Advanced Mathematics 8) , 1988 .

[13]  Kazuya Kato,et al.  Duality theories for p-primary etale cohomology III , 2018, 1810.02218.

[14]  S. Saito.  Class Field Theory for Two Dimensional Local Rings , 1987 .

[15]  M. Reid,et al.  Commutative ring theory: Regular rings , 1987 .

[16]  S. Bloch,et al.  p-Adic etale cohomology , 1986 .

[17]  J. Milne.  VALUES OF ZETA FUNCTIONS OF VARIETIES OVER FINITE FIELDS , 1986 .

[18]  Kazuya Kato.  A Hasse principle for two dimensional global fields. , 1986 .

[19]  Dorin Popescu,et al.  General Néron desingularization , 1985, Nagoya Mathematical Journal.

[20]  M. Gros.  Classes de Chern et classes de cycles en cohomologie de Hodge-Witt logarithmique , 1985 .

[21]  T. Ekedahl.  On the multiplicative properties of the de Rham—Witt complex. I , 1984 .

[22]  L. Illusie,et al.  Les suites spectrales associées au complexe de de Rham-Witt , 1983 .

[23]  J. Colliot-Thélène,et al.  TORSION DANS LE GROUPE DE CHOW DE CODIMENSION DEUX , 1983 .

[24]  L. Illusie.  Complexe de de Rham-Witt et cohomologie cristalline , 1979 .

[25]  S. Bloch.  Algebraic K-theory and crystalline cohomology , 1977 .

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

[27]  E. Kunz.  ON NOETHERIAN RINGS OF CHARACTERISTIC p. , 1976 .

[28]  J. Milne.  Duality in the flat cohomology of a surface , 1976 .

[29]  Pierre Berthelot,et al.  Cohomologie cristalline des sch'emas de caract'eristique p > 0 , 1974 .

[30]  A. Ogus,et al.  Gersten's conjecture and the homology of schemes , 1974 .

[31]  H. Bass,et al.  The Milnor ring of a global field , 1973 .

[32]  D. Gorenstein,et al.  Algebraic approximation of structures over complete local rings , 1969 .

[33]  R. Hartshorne.  Residues And Duality , 1966 .