Algebraic $K$-theory and crystalline cohomology

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1. [1] M. ARTIN and B. MAZUR, Formal groups arising from algebraic varieties (preprint). Zbl0351.14023
2. [1 bis] M. ARTIN, Supersingular K-3 surfaces, Annales E.N.S., t. 7 (1974), pp. 543-568. Zbl0322.14014MR51 #8116
3. [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. 
4. [3] P. BERTHELOT, Cohomologie Cristalline des Schémas de Caractéristique p > o, Lecture Notes in Math., n° 407, Berlin, Springer, 1974. Zbl0298.14012MR52 #5676
5. [3 bis] P. BERTHELOT, Slopes of Frobenius in crystalline cohomology, Proc. Symp. Pure Math., vol. XXIX (1975), pp. 315-328. Zbl0323.14008MR52 #3167
6. [3 ter] P. BERTHELOT, SGA 6, Exposé V, Lecture Notes in Math., n° 225, Berlin, Springer, 1971. MR50 #7133
7. [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. Zbl0198.26201MR42 #4555
8. [5] S. BLOCH, K2 and algebraic cycles, Annals of Math., vol. 99 (1974), pp. 349-379. Zbl0298.14005MR49 #7260
9. [6] S. BLOCH, On the tangent space to Quillen K-theory, Algebraic K-theory I, Lecture Notes in Math., n° 341, Berlin, Springer, 1973. Zbl0287.18016MR57 #6144
10. [7] K. BROWN, private correspondence. 
11. [8] P. CARTIER, Groupes formels associés aux anneaux de Witt généralisés, Comptes rendus Acad. Sc. Paris, t. 265 (1967), pp. 50-52. Zbl0168.27501MR36 #1448
12. [9] P. CARTIER, Modules associés à un groupe formel commutatif. Courbes typiques, Comptes rendus Acad. Sc. Paris, t. 265 (1967), pp. 129-132. Zbl0168.27502MR36 #1449
13. [10] P. CARTIER, Relèvements des groupes formels commutatifs, Séminaire Bourbaki, n° 359 (1968-1969) ; Lecture Notes in Math., n° 179, Berlin, Springer, 1971. Zbl0215.37401
14. [11] P. CARTIER, Questions de rationalité des diviseurs en géométrie algébrique, Bull. Soc. Math. France, 86 (1958), pp. 177-251. Zbl0091.33501MR21 #4957
15. [12] M. DEMAZURE, Lectures on p-divisible groups, Lecture Notes in Math., n° 302, Berlin, Springer, 1972. Zbl0247.14010MR49 #9000
16. [13] A. DOLD and D. PUPPE, Homologie nicht-additiver Functoren. Anwendungen, Ann. Inst. Fourier, 11 (1961), pp. 201-312. Zbl0098.36005MR27 #186
17. [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. Zbl0289.18011
18. [15] S. GERSTEN, Products in algebraic K-theory (preprint). 
19. [15 bis] S. GERSTEN, The localization theorem for projective modules (preprint). Zbl0332.18013
20. [16] A. GROTHENDIECK, Crystals and the de Rham cohomology of schemes, in Dix exposés sur la cohomologie des schémas, Amsterdam, North Holland, 1968. Zbl0215.37102MR42 #4558
21. [17] A. GROTHENDIECK, S.G.A. VI, Exposé o, Lecture Notes in Math., n° 225, Berlin, Springer, 1971. MR50 #7133
22. [18] A. GROTHENDIECK, Classes de Chern et représentations linéaires des groupes discrets, in Dix exposés sur la cohomologie des schémas, Amsterdam, North Holland, 1968. Zbl0198.26101MR42 #280
23. [19] A. GROTHENDIECK, S.G.A. IV, Exposé 3, Lecture Notes in Math., n° 269, Berlin, Springer, 1972. 
24. [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). 
25. [20 bis] A. GROTHENDIECK, Groupe de Brauer III, in Dix exposés sur la cohomologie des schémas, Amsterdam, North Holland, 1968. Zbl0198.25901
26. [21] L. ILLUSIE, letter to Gersten. 
27. [21 bis] L. ILLUSIE, Report on Crystalline cohomology, Proc. Symp. Pure Math., vol. XXIX (1975), pp. 459-478. Zbl0326.14005MR52 #13845
28. [22] S. LUBKIN, Generalization of p-adic cohomology (preprint). Zbl0368.14009
29. [23] J. MANIN, The theory of commutative formal groups over fields of finite characteristic, English translation, Russian Math. Surveys, 18, 1963. Zbl0128.15603MR28 #1200
30. [23 bis] B. MAZUR, Frobenius and the Hodge filtration, Bull. A.M.S., 78 (1972), pp. 653-667. Zbl0258.14006MR48 #8507
31. [24] D. QUILLEN, Higher Algebraic K-theory I, Algebraic K-theory I, Lecture Notes in Math., n° 341, Berlin, Springer, 1973. Zbl0292.18004MR49 #2895
32. [25] J.-P. SERRE, Sur la topologie des variétés algébriques en charactéristique p, Symposium Internacional de Topologia Algebraica, Mexico (1958), pp. 24-53. Zbl0098.13103MR20 #4559
33. [26] M. STEIN, Surjective stability in dimension o for K2 and related functors, Trans. A.M.S. (to appear). Zbl0267.18015
34. [27] W. VAN DER KALLEN, Le K2 des nombres duaux, Comptes rendus Acad. Sc. Paris, t. 273 (1971), 1204-1207. Zbl0225.13006MR45 #252
35. [28] K. DENNIS and M. STEIN, K2 of discrete valuation rings (to appear). Zbl0318.13017
36. [29] K. DENNIS, private correspondence. 
37. [30] J. MILNOR, Introduction to Algebraic K-theory, Annals of Math. Studies, n° 72, Princeton University Press, 1971. Zbl0237.18005MR50 #2304
38. [31] D. MUMFORD, Curves on an Algebraic Surface, Annals of Math. Studies, n° 59, Princeton University Press, 1966. Zbl0187.42701MR35 #187
39. [32] J.-L. LODAY, K-théorie algébrique et représentations de groupes, thèse, Université Louis-Pasteur, Strasbourg, 1975. MR54 #8675
40. [33] H. BASS, Algebraic K-theory, New York, Benjamin, 1968. Zbl0174.30302MR40 #2736

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