p -adic etale cohomology

Spencer Bloch; Kazuya Kato

Publications Mathématiques de l'IHÉS (1986)

  • Volume: 63, page 107-152
  • ISSN: 0073-8301

How to cite


Bloch, Spencer, and Kato, Kazuya. "$p$-adic etale cohomology." Publications Mathématiques de l'IHÉS 63 (1986): 107-152. <http://eudml.org/doc/104010>.

author = {Bloch, Spencer, Kato, Kazuya},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {étale cohomology groups; de Rham-Witt cohomology groups; crystalline cohomology groups; Hodge-Tate decomposition},
language = {eng},
pages = {107-152},
publisher = {Institut des Hautes Études Scientifiques},
title = {$p$-adic etale cohomology},
url = {http://eudml.org/doc/104010},
volume = {63},
year = {1986},

AU - Bloch, Spencer
AU - Kato, Kazuya
TI - $p$-adic etale cohomology
JO - Publications Mathématiques de l'IHÉS
PY - 1986
PB - Institut des Hautes Études Scientifiques
VL - 63
SP - 107
EP - 152
LA - eng
KW - étale cohomology groups; de Rham-Witt cohomology groups; crystalline cohomology groups; Hodge-Tate decomposition
UR - http://eudml.org/doc/104010
ER -


  1. [1] BASS, H., and TATE, J., The Milnor ring of a global field, in Algebraic K-theory, II, Springer Lecture Notes in Math., 342 (1972), 349-442. Zbl0299.12013MR56 #449
  2. [2] BERTHELOT, P., Cohomologie cristalline des schémas de charactéristique p &gt; 0, Springer Lecture Notes in Math., 407 (1974). Zbl0298.14012MR52 #5676
  3. [3] BLOCH, S., Algebraic K-theory and crystalline cohomology, Publ. Math. I.H.E.S., 47 (1974), 187-268. Zbl0388.14010MR81j:14011
  4. [4] BLOCH, S., Torsion algebraic cycles, K2, and Brauer groups of function fields, in Groupe de Brauer, Springer Lecture Notes in Math., 844 (1981), 75-102. Zbl0467.12011MR82k:14018
  5. [5] BLOCH, S., p-adic étale cohomology, in Arithmetic and Geometry, vol. I, 13-27, Birkhäuser (1983). Zbl0584.14009MR85b:14026
  6. [6] DELIGNE, P. (with ILLUSIE, L.), Cristaux ordinaires et coordonnées canoniques, in Surfaces algébriques, Springer Lecture Notes in Math., 868 (1981), 80-137. Zbl0537.14012MR83k:14039a
  7. [7] GABBER, O., An injectivity property for étale cohomology, preprint, 1981. Zbl0828.14011
  8. [8] GABBER, O., Gersten's conjecture for some complexes of vanishing cycles, preprint, 1981. Zbl0827.19002
  9. [9] GABBER, O., Affine analog of proper base change theorem, preprint, 1981. Zbl0816.13006
  10. [10] ILLUSIE, L., Complexe de De Rham-Witt et cohomologie cristalline, Ann. Sci. Ec. Norm. Sup., 4e sér., 12 (1979), 501-661. Zbl0436.14007MR82d:14013
  11. [11] KATO, K., A generalization of local class field theory by using K-groups, II, J. Fac. Sci. Univ. Tokyo, 27 (1980), 603-683. Zbl0463.12006MR83g:12020a
  12. [12] KATO, K., Galois cohomology of complete discrete valuation fields, in Algebraic K-theory, Springer Lecture Notes in Math., 967 (1982), 215-238. Zbl0506.12022MR84k:12006
  13. [13] KATZ, N., Serre-Tate local moduli, in Surfaces algébriques, Springer Lecture Notes in Math., 868 (1981), 138-202. Zbl0477.14007MR83k:14039b
  14. [14] MERKURJEV, A. S., and SUSLIN, A. A., K-cohomology of Severi-Brauer varieties and norm residue homomorphism, Math. U.S.S.R. Izvestiya, 21 (1983), 307-340. Zbl0525.18008
  15. [15] MILNOR, J., Algebraic K-theory and quadratic forms, Inv. Math., 9 (1970), 318-344. Zbl0199.55501MR41 #5465
  16. [16] SERRE, J.-P., Cohomologie Galoisienne, Springer Lecture Notes in Math., 5 (1965). Zbl0136.02801MR34 #1328
  17. [17] SOULÉ, C., K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Inv. Math., 55 (1979), 251-295. Zbl0437.12008MR81i:12016
  18. [18] TATE, J., p-divisible groups, in Proceedings of a Conference on local fields, Springer-Verlag, 1967, 158-183. Zbl0157.27601MR38 #155
  19. [19] TATE, J., Relation between K2 Galois cohomology, Inv. Math., 36 (1976), 257-274. Zbl0359.12011MR55 #2847
  20. [20] DELIGNE, P., La conjecture de Weil, II, Publ. Math. I.H.E.S., 52 (1980), 313-428. Zbl0456.14014MR83c:14017
  21. [21] ILLUSIE, L., and RAYNAUD, M., Les suites spectrales associées au complexe de De Rham-Witt, Publ. Math. I.H.E.S., 57 (1983), 73-212. Zbl0538.14012MR85e:14026
  22. [22] SERRE, J.-P., Sur les corps locaux à corps résiduel algébriquement clos, Bull. Soc. Math. France, 8 (1961), 105-154. Zbl0166.31103MR26 #103

Citations in EuDML Documents

  1. Ofer Gabber, An injectivity property for étale cohomology
  2. Takako Kuzumaki, The cohomological dimension of the quotient field of the two dimensional complete local domain
  3. M. Rapoport, M. Richartz, On the classification and specialization of F -isocrystals with additional structure
  4. Masato Kurihara, On two types of complete discrete valuation fields
  5. Paul Arne Østvær, Periodicity in K -groups of certain fields
  6. Victor Abrashkin, Ruth Jenni, The field-of-norms functor and the Hilbert symbol for higher local fields
  7. Kazuya Kato, The explicit reciprocity law and the cohomology of Fontaine-Messing
  8. Takeshi Tsuji, On the p adic nearby cycles of log smooth families
  9. Bruno Kahn, La conjecture de Milnor
  10. Ahmed Abbes, Abdellah Mokrane, Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.