Algebraic K-theory and crystalline cohomology
Publications Mathématiques de l'IHÉS, Tome 47 (1977), pp. 187-268.
@article{PMIHES_1977__47__187_0,
     author = {Bloch, Spencer},
     title = {Algebraic $K$-theory and crystalline cohomology},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {187--268},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {47},
     year = {1977},
     mrnumber = {488288},
     zbl = {0388.14010},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1977__47__187_0/}
}
TY  - JOUR
AU  - Bloch, Spencer
TI  - Algebraic $K$-theory and crystalline cohomology
JO  - Publications Mathématiques de l'IHÉS
PY  - 1977
SP  - 187
EP  - 268
VL  - 47
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1977__47__187_0/
LA  - en
ID  - PMIHES_1977__47__187_0
ER  - 
%0 Journal Article
%A Bloch, Spencer
%T Algebraic $K$-theory and crystalline cohomology
%J Publications Mathématiques de l'IHÉS
%D 1977
%P 187-268
%V 47
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1977__47__187_0/
%G en
%F PMIHES_1977__47__187_0
Bloch, Spencer. Algebraic $K$-theory and crystalline cohomology. Publications Mathématiques de l'IHÉS, Tome 47 (1977), pp. 187-268. http://www.numdam.org/item/PMIHES_1977__47__187_0/

[1] M. Artin and B. Mazur, Formal groups arising from algebraic varieties (preprint). | Numdam | Zbl

[1 bis] M. Artin, Supersingular K-3 surfaces, Annales E.N.S., t. 7 (1974), pp. 543-568. | EuDML | Numdam | MR | Zbl

[2] P. Berthelot, Notes in the Comptes Rendus Acad. Sc. Paris, t. 269 (1969), pp. 297-300, 357-360, 397-400; t. 272 (1971), pp. 141-144, 1314-1317, 1397-1400.

[3] P. Berthelot, Cohomologie Cristalline des Schémas de Caractéristique p > o, Lecture Notes in Math., n° 407, Berlin, Springer, 1974. | MR | Zbl

[3 bis] P. Berthelot, Slopes of Frobenius in crystalline cohomology, Proc. Symp. Pure Math., vol. XXIX (1975), pp. 315-328. | MR | Zbl

[3 ter] P. Berthelot, SGA 6, Exposé V, Lecture Notes in Math., n° 225, Berlin, Springer, 1971. | MR

[4] P. Berthelot and L. Illusie, Classes de Chern en cohomologie cristalline, Comptes Rendus Acad. Sc. Paris, t. 270 (1970), pp. 1695-1697, 1750-1752. | MR | Zbl

[5] S. Bloch, K2 and algebraic cycles, Annals of Math., vol. 99 (1974), pp. 349-379. | MR | Zbl

[6] S. Bloch, On the tangent space to Quillen K-theory, Algebraic K-theory I, Lecture Notes in Math., n° 341, Berlin, Springer, 1973. | MR | Zbl

[7] K. Brown, private correspondence.

[8] P. Cartier, Groupes formels associés aux anneaux de Witt généralisés, Comptes rendus Acad. Sc. Paris, t. 265 (1967), pp. 50-52. | MR | Zbl

[9] P. Cartier, Modules associés à un groupe formel commutatif. Courbes typiques, Comptes rendus Acad. Sc. Paris, t. 265 (1967), pp. 129-132. | MR | Zbl

[10] P. Cartier, Relèvements des groupes formels commutatifs, Séminaire Bourbaki, n° 359 (1968-1969) ; Lecture Notes in Math., n° 179, Berlin, Springer, 1971. | Numdam | Zbl

[11] P. Cartier, Questions de rationalité des diviseurs en géométrie algébrique, Bull. Soc. Math. France, 86 (1958), pp. 177-251. | Numdam | MR | Zbl

[12] M. Demazure, Lectures on p-divisible groups, Lecture Notes in Math., n° 302, Berlin, Springer, 1972. | MR | Zbl

[13] A. Dold and D. Puppe, Homologie nicht-additiver Functoren. Anwendungen, Ann. Inst. Fourier, 11 (1961), pp. 201-312. | Numdam | MR | Zbl

[14] S. Gersten, Higher K-theory of rings ; and Some exact sequences in the higher K-theory of rings, Algebraic K-theory I, Lecture Notes in Math., n° 341, Berlin, Springer, 1973. | Zbl

[15] S. Gersten, Products in algebraic K-theory (preprint).

[15 bis] S. Gersten, The localization theorem for projective modules (preprint). | Zbl

[16] A. Grothendieck, Crystals and the de Rham cohomology of schemes, in Dix exposés sur la cohomologie des schémas, Amsterdam, North Holland, 1968. | MR | Zbl

[17] A. Grothendieck, S.G.A. VI, Exposé o, Lecture Notes in Math., n° 225, Berlin, Springer, 1971. | MR

[18] A. Grothendieck, Classes de Chern et représentations linéaires des groupes discrets, in Dix exposés sur la cohomologie des schémas, Amsterdam, North Holland, 1968. | MR | Zbl

[19] A. Grothendieck, S.G.A. IV, Exposé 3, Lecture Notes in Math., n° 269, Berlin, Springer, 1972.

[20] A. Grothendieck, J. Dieudonné, Éléments de géométrie algébrique, Publ. Math. I.H.E.S., 4, 8, 11, 17, 20, 24, 28, 32 (1959-1967). | Numdam

[20 bis] A. Grothendieck, Groupe de Brauer III, in Dix exposés sur la cohomologie des schémas, Amsterdam, North Holland, 1968. | Zbl

[21] L. Illusie, letter to Gersten.

[21 bis] L. Illusie, Report on Crystalline cohomology, Proc. Symp. Pure Math., vol. XXIX (1975), pp. 459-478. | MR | Zbl

[22] S. Lubkin, Generalization of p-adic cohomology (preprint).

[23] J. Manin, The theory of commutative formal groups over fields of finite characteristic, English translation, Russian Math. Surveys, 18, 1963. | MR | Zbl

[23 bis] B. Mazur, Frobenius and the Hodge filtration, Bull. A.M.S., 78 (1972), pp. 653-667. | MR | Zbl

[24] D. Quillen, Higher Algebraic K-theory I, Algebraic K-theory I, Lecture Notes in Math., n° 341, Berlin, Springer, 1973. | MR | Zbl

[25] J.-P. Serre, Sur la topologie des variétés algébriques en charactéristique p, Symposium Internacional de Topologia Algebraica, Mexico (1958), pp. 24-53. | MR | Zbl

[26] M. Stein, Surjective stability in dimension o for K2 and related functors, Trans. A.M.S. (to appear). | Zbl

[27] W. Van Der Kallen, Le K2 des nombres duaux, Comptes rendus Acad. Sc. Paris, t. 273 (1971), 1204-1207. | MR | Zbl

[28] K. Dennis and M. Stein, K2 of discrete valuation rings (to appear).

[29] K. Dennis, private correspondence.

[30] J. Milnor, Introduction to Algebraic K-theory, Annals of Math. Studies, n° 72, Princeton University Press, 1971. | MR | Zbl

[31] D. Mumford, Curves on an Algebraic Surface, Annals of Math. Studies, n° 59, Princeton University Press, 1966. | MR | Zbl

[32] J.-L. Loday, K-théorie algébrique et représentations de groupes, thèse, Université Louis-Pasteur, Strasbourg, 1975. | MR

[33] H. Bass, Algebraic K-theory, New York, Benjamin, 1968. | MR | Zbl