Torsion étale and crystalline cohomologie

Breuil, Christophe ; Messing, William

Cohomologies

p

-adiques et applications arithmétiques (II), Astérisque, no. 279 (2002), pp. 81-124.

MR Zbl | 1 citation dans Numdam

@incollection{AST_2002__279__81_0,
     author = {Breuil, Christophe and Messing, William},
     title = {Torsion \'etale and crystalline cohomologie},
     booktitle = {Cohomologies $p$-adiques et applications arithm\'etiques (II)},
     editor = {Berthelot Pierre and Fontaine Jean-Marc and Illusie Luc and Kato Kazuya and Rapoport Michael},
     series = {Ast\'erisque},
     pages = {81--124},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {279},
     year = {2002},
     mrnumber = {1922829},
     zbl = {1035.14005},
     language = {en},
     url = {https://numdam.org/item/AST_2002__279__81_0/}
}

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%A Messing, William
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%B Cohomologies $p$-adiques et applications arithmétiques (II)
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%E Fontaine Jean-Marc
%E Illusie Luc
%E Kato Kazuya
%E Rapoport Michael
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Breuil, Christophe; Messing, William. Torsion étale and crystalline cohomologie, dans Cohomologies $p$-adiques et applications arithmétiques (II), Astérisque, no. 279 (2002), pp. 81-124. https://numdam.org/item/AST_2002__279__81_0/

Bibliographie
Cité par

[1] Abrashkin V., Ramification in étale cohomology, Inv. Math. 101, 1990, 631-640. | DOI | EuDML | MR | Zbl

[2] Berthelot P., Slopes of Frobenius in crystalline cohomology, Proc. of Symposia in Pure Maths. 29, Americ. Math. Soc., 1975, 315-328. | DOI | MR | Zbl

[3] Berthelot P., Cohomologie cristalline des schémas de caractéristique $p > 0$ , Lecture Notes in Math. 407, Springer-Verlag, Berlin, 1974. | MR | Zbl

[4] Berthelot P., Ogus A., Notes on crystalline cohomology, Princeton University Press, Princeton, 1978. | MR | Zbl

[5] Berthelot P., Ogus A., $F$ -isocristals and de Rham cohomology I, Inv. Math. 72, 1983, 159-199. | DOI | EuDML | MR | Zbl

[6] Bloch S., Kato K., $p$ -adic étale cohomology, Pub. Math, de l'I.H.E.S. 63, 1986, 107-152. | DOI | EuDML | Numdam | MR | Zbl

[7] Breuil C, Topologie log-syntomique, cohomologie log-cristalline et cohomologie de Čech, Bull. Soc. math. France 124, 1996, 587-647. | DOI | EuDML | Numdam | MR | Zbl

[8] Breuil C , Représentations $p$ -adiques semi-stables et transversalité de Griffiths, Math. Annalen 307, 1997, 191-224. | DOI | MR | Zbl

[9] Breuil C , Construction de représentations $p$ -adiques semi-stables, Ann. Scient. de l'E.N.S. 31, 1998, 281-327. | EuDML | Numdam | MR | Zbl

[10] Breuil C., Cohomologie étale de $p$ -torsion et cohomologie cristalline en réduction semi-stable, Duke Math. J. 95, 1998, 523-620. | DOI | MR | Zbl

[11] Breuil C., Représentations semi-stables et modules fortement divisibles, Inv. Math. 136, 1999, 89-122. | DOI | MR | Zbl

[12] Breuil C., Une remarque sur les représentations locales $p$ -adiques et les congruences entre formes modulaires de Hilbert, Bull. Soc. Math. France 127, 1999, 459-472. | DOI | EuDML | Numdam | MR | Zbl

[13] Breuil C., Letter to Gross, December 3, 1998.

[14] Colmez P., Fontaine J.-M., Construction des représentations $p$ -adiques semi-stables, Inv. Math. 140, 2000, 1-43. | DOI | MR | Zbl

[15] Conrad B., Diamond F., Taylor R., Modularity of certain potentially crystalline Galois representations, J. Amer. Math. Soc. 12, 1999, 521-567. | DOI | MR | Zbl

[16] Deligne P., Illusie L., Relèvement modulo $p^{2}$ et décomposition du complexe de de Rham, Inv. Math. 89, 1987, 247-270. | DOI | EuDML | MR | Zbl

[17] Ekedahl T., Diagonal complexes and $F$ -gauges structures, Travaux en cours, Hermann, Paris, 1986. | MR | Zbl

[18] Faltings G., $p$ -adic Hodge theory, J. Amer. Math. Soc. 1, 1988, 255-299. | MR | Zbl

[19] Faltings G., Crystalline cohomology and $p$ -adic Galois representations, Algebraic Analysis, Geometry and Number Theory, Johns Hopkins Univ. Press, 1989, 25-79. | MR | Zbl

[20] Faltings G., Crystalline cohomology of semi-stable curves, and $p$ -adic Galois representations, Journal of Algebraic Geometry 1, 1992, 61-82, correction, 427. | MR | Zbl

[21] Faltings G., Integral crystalline cohomology over very ramified valuation rings, J. Amer. Math. Soc. 12, 1999, 117-144. | DOI | MR | Zbl

[22] Faltings G., Almost étale extensions, these proceedings.

[23] Faltings G., Jordan B., Crystalline cohomology and $G L_{2} (𝐐)$ , Isr. J. of Math. 90, 1995, 1-66. | MR | Zbl

[24] Fontaine J.-M., Le corps des périodes $p$ -adiques, Astérisque 223, Soc. Math. de France, 1994, 59-111. | Numdam | MR | Zbl

[25] Fontaine J.-M., Représentations $p$ -adiques semi-stables, Astérisque 223, Soc. Math. de France, 1994, 113-184. | Numdam | MR | Zbl

[26] Fontaine J.-M., Schémas propres et lisses sur $𝐙$ , Proceedings of the Indo-French Conference on Geometry, Hindustan Book Agency, 1993, 43-56. | MR | Zbl

[27] Fontaine J.-M., Cohomologie de de Rham, cohomologie cristalline et représentations $p$ -adiques, Lecture Notes in Maths 1016, 1983, 86-108. | MR | Zbl

[28] Fontaine J.-M., Il n'y a pas de variétés abéliennes sur $𝐙$ , Inv. Math. 81, 1985, 515-538. | DOI | EuDML | MR | Zbl

[29] Fontaine J.-M., Groupes finis commutatifs sur les vecteurs de Witt, C.R.A.S. 280, 1975, 1423-1425. | MR | Zbl

[30] Fontaine J.-M., Sur certains types de représentations $p$ -adiques du groupe de Galois d'un corps local ; construction d'un anneau de Barsotti-Tate, Ann. of Maths 115, 1982, 379-409. | MR | Zbl

[31] Fontaine J.-M., Laffaille G., Construction de représentations $p$ -adiques, Ann. Scient. de l'E.N.S. 15, 1982, 547-608. | EuDML | Numdam | MR | Zbl

[32] Fontaine J.-M., Messing W., $p$ -adic periods and $p$ -adic étale cohomology, Contemporary Math. 67, 1987, 179-207. | DOI | MR | Zbl

[33] Gross B., Letter to Wintenberger, December 2, 1997.

[34] Grothendieck A., Fondements de la Géometrie Algébrique, extracts from Séminaire Bourbaki 1957-1962. | MR | Zbl

[35] Grothendieck A., Crystals and de Rham cohomology of schemes, Dix exposés sur la cohomologie des schémas, North Holland, 1968, 306-358. | MR | Zbl

[36] Grothendieck A., Letter to Deligne, October 10, 1965.

[37] Hyodo O., A note on $p$ -adic étale cohomology in the semi-stable reduction case, Inv. Math. 91, 1988, 543-557. | DOI | EuDML | MR | Zbl

[38] Hyodo O., Kato K., Semi-stable reduction and crystalline cohomology with logarithmic poles, Astérisque 223, Soc. Math. de France, 1994, 221-268. | Numdam | MR | Zbl

[39] Illusie L., Logarithmic smoothness and vanishing cycles, preprint, Université Paris-Sud, 1995.

[40] Illusie L., An overview of the work of K. Fujiwara, K. Kato and C. Nakayama on Logarithmic Etale Cohomology, these proceedings.

[41] Illusie L., Cohomologie de de Rham et cohomologie étale $p$ -adique [d'après G.Faltings, J.-M. Fontaine et al.], Séminaire Bourbaki 726, 1990. | EuDML | Numdam | MR | Zbl

[42] Jordan B., Higher weight modular forms and Galois representations, Contemporary Mathematics 165, 1994, 175-181. | DOI | MR | Zbl

[43] Kato K., Logarithmic structures of Fontaine-Illusie, Algebraic Analysis, Geometry and Number Theory, John Hopkins University Press, 1989, 191-224. | MR | Zbl

[44] Kato K., Semi-stable reduction and $p$ -adic étale cohomology, Astérisque 223, Soc. Math. de France, 1994, 269-293. | Numdam | MR | Zbl

[45] Kato K., On $p$ -adic Vanishing Cycles (Application of ideas of Fontaine-Messing), Advanced Studies in Pure Maths. 10, 1987, 207-251. | DOI | MR | Zbl

[46] Kato K., Messing W., Syntomic cohomology and p-adic étale cohomology, Tôhoku Math. J. 44, 1992, 1-9. | DOI | MR | Zbl

[47] Kurihara M., A note on $p$ -adic étale cohomology, Proc. Japan Acad. 63, 1987, 275-278. | DOI | MR | Zbl

[48] Laffaille G., Groupes $p$ -divisibles et modules filtrés: le cas peu ramifié, Bull. Soc. math. France 108, 1980, 187-206. | DOI | EuDML | Numdam | MR | Zbl

[49] Mazur B., Frobenius and the Hodge filtration, Bull. Amer. Math. Soc. 78, 1972, 653-667. | DOI | MR | Zbl

[50] Mazur B., Frobenius and the Hodge filtration-estimates, Ann. of Math. 98, 1973, 58-95. | DOI | MR | Zbl

[51] Mazur B., Notes on syntomic sites, typed notes.

[52] Mazur B., Deforming Galois representations, in Galois Groups over $𝐐$ , Springer 1989, 385-438. | MR | Zbl

[53] Mazur B., Letter to Breuil, July 26, 1996.

[54] Mokrane A., Quelques remarques sur l'ordinarité, J. of Number Theory 73, 1998, 162-181. | DOI | MR | Zbl

[55] Mumford D., Pathologies of modular algebraic surfaces, Amer. J. of Math. 83, 1961, 339-342. | DOI | MR | Zbl

[56] Mumford D., Further pathologies in Algebraic Geometry, Amer. J. of Math. 84, 1962, 642-648. | DOI | MR | Zbl

[57] Nakayama C., Logarithmic etale cohomology, Math. Ann. 308, 1997, 365-404. | DOI | MR | Zbl

[58] Nakayama C., Nearby cycles for log smooth families, Comp. Math. 112, 1998, 45-75. | DOI | MR | Zbl

[59] Niziol W., Crystalline conjecture via $K$ -theory, Ann. Scient. de l'E.N.S. 31, 1998, 659-681. | EuDML | Numdam | MR | Zbl

[60] Quiros A., On the divisibility properties of families of filtered $F$ -crystals, Math. Ann. 288, 1990, 389-412. | DOI | EuDML | MR | Zbl

[61] Ramakrishna R., On a variation of Mazur's deformation functor, Comp. Math. 87, 1993, 269-286. | EuDML | Numdam | MR | Zbl

[62] Raynaud M., $p$ -torsion du schéma de Picard, Journées de Géométrie algébrique de Rennes, Astérisque 64, Soc. Math, de France, 1979, 87-148. | Numdam | MR | Zbl

[63] Rapoport M., Zink T., Üeber die lokale Zetafunktion von Shimuravarietäten, Monodromiefiltration und verschwindende Zyklen in ungleicher Characteristik, Inv. Math. 68, 1982, 21-101. | DOI | EuDML | MR | Zbl

[64] Serre J.-P., Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Inv. Math. 15, 1972, 259-331. | DOI | EuDML | MR | Zbl

[65] Serre J.-P., Sur les représentations modulaires de $Gal (\bar{𝐐} / 𝐐)$ , Duke Math. J. 54, 1987, 179-230. | MR | Zbl

[66] Serre J.-P., Corps locaux, troisième édition, Hermann, 1968. | MR

[67] Serre J.-P., Séminaire du cours au Collège de France, 1960.

[68] De Smit B., Lenstra H. W., Explicit construction of universal deformation rings, Modular forms and Fermat's Last Theorem, Springer, 1997, 313-326. | DOI | MR | Zbl

[69] Tsuji T., Syntomic complexes and $p$ -adic vanishing cycles, J. reine angew. Math. 472, 1996, 69-138. | EuDML | MR | Zbl

[70] Tsuji T., $p$ -adic-étale cohomology and crystalline cohomology in the semi-stable reduction case, Inv. Math. 137, 1999, 233-411. | DOI | MR | Zbl

[71] Tsuji T., Semi-stable conjecture of Fontaine-Jannsen: a survey, these proceedings.

[72] Tsuji T., $p$ -adic Hodge theory in the semi-stable reduction case, Proceedings of the ICM 1998, Vol. II, 207-216. | EuDML | MR | Zbl

[73] Tsuzuki N., On filtered modules and $p$ -adic representations of finite length over a local field with mixed characteristic, Master's thesis, Tokyo, 1990.

[74] Ulmer D., Slopes of modular forms and congruences, Ann. Inst. Fourier 46, 1996, 1-32. | DOI | EuDML | Numdam | MR | Zbl

[75] Wach N., Représentations cristallines de torsion, Comp. Math. 108, 1997, 185-240. | DOI | MR | Zbl