Semi-stable conjecture of Fontaine-Jannsen : a survey

Tsuji, Takeshi

Cohomologies

p

-adiques et applications arithmétiques (II), Astérisque, no. 279 (2002), pp. 323-370.

MR Zbl | 4 citations dans Numdam

@incollection{AST_2002__279__323_0,
     author = {Tsuji, Takeshi},
     title = {Semi-stable conjecture of {Fontaine-Jannsen} : a survey},
     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 = {323--370},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {279},
     year = {2002},
     mrnumber = {1922833},
     zbl = {1041.14003},
     language = {en},
     url = {http://www.numdam.org/item/AST_2002__279__323_0/}
}

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Tsuji, Takeshi. Semi-stable conjecture of Fontaine-Jannsen : a survey, dans Cohomologies $p$-adiques et applications arithmétiques (II), Astérisque, no. 279 (2002), pp. 323-370. http://www.numdam.org/item/AST_2002__279__323_0/

Bibliographie
Cité par

[Ber74] P. Berthelot - Cohomologie cristalline des schémas de caractéristique $p > 0$ , Lecture Notes in Math. 407, Springer, 1974. | MR | Zbl

[BK86] S. Bloch & K. Kato - $p$ -adic etale cohomology, Publ Math. IHES. 63 (1986), p. 107-152. | DOI | EuDML | Numdam | MR | Zbl

[BM] C. Breuil & W. Messing - Torsion etale and crystalline cohomologies, these proceedings.

[B078] P. Berthelot & A. Ogus - Notes on crystalline cohomology, Princeton University Press, 1978. | MR | Zbl

[B083] P. Berthelot & A. Ogus, $F$ -isocrystals and de Rham cohomology I, Invent math. 72 (1983), p. 159-199. | DOI | EuDML | MR | Zbl

[Bre96] C. Breuil - Topologie log-syntomique, cohomologie log-cristalline et cohomologie de Čech, Bull Soc. math. France 124 (1996), p. 587-647. | DOI | EuDML | Numdam | MR | Zbl

[Bre98a] C. Breuil, Construction de représentations $p$ -adiques semi-stables, Ann. Scient. E. N. S. 31 (1998), p. 281-327. | EuDML | Numdam | MR | Zbl

[Bre98b] C. Breuil, Cohomologie étale de $p$ -torsion et cohomologie cristalline en réduction semi-stable, Duke Math. J. 95 (1998), p. 523-620. | DOI | MR | Zbl

[dJ96] A. J. De Jong - Smoothness, semi-stability and alterations, Publ. Math. IHES 83 (1996), p. 51-93. | DOI | EuDML | Numdam | MR | Zbl

[Fal88] G. Faltings - $p$ -adic Hodge theory, Journal of the AMS 1(1988), p. 255-299. | MR | Zbl

[Fal89] G. Faltings, Crystalline cohomology and $p$ -adic Galois representations, Algebraic analysis, geometry, and number theory, Johns Hopkins University Press, Baltimore, 1989, p. 25-80. | MR | Zbl

[Fal92] G. Faltings, Crystalline cohomology of semi-stable curves, and $p$ -adic Galois representations, Journal of Algebraic Geometry 1(1992), p. 61-82. | MR | Zbl

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

[FI93] J.-M. Fontaine & L. Illusie - $p$ -adic periods: a survey, Proceedings of the Indo-Prench Conference on Geometry (Bombay, 1989), Hindustan Book Agency, Delhi, 1993, p. 57-93. | MR | Zbl

[FL82] J.-M. Fontaine & G. Laffaille - Constructions de représentations $p$ -adiques, Ann. Sci. Éc. Norm. Sup. 15 (1982), p. 547-608. | DOI | EuDML | Numdam | MR | Zbl

[FM87] J.-M. Fontaine & W. Messing - $p$ -adic periods and p-adic étale cohomology, Contemporary Math. 67, 1987, p. 179-207. | DOI | MR | Zbl

[Fon82] J.-M. Fontaine - Sur certains types de représentations $p$ -adiques du groupe de Galois d'un corps local; construction d'un anneau de Barsotti-Tate, Ann. of Math. 115 (1982), p. 529-577. | DOI | MR | Zbl

[Fon83] J.-M. Fontaine, Cohomologie de de Rham, cohomologie cristalline et représentations $p$ -adiques, Algebraic Geometry, Lecture Notes in Math. 1016, Springer, 1983, p. 86-108. | DOI | MR | Zbl

[Fon94a] J.-M. Fontaine, Le corps des périodes $p$ -adiques, Périodes $p$ -adiques, Séminaire de Bures 1988, Astérisque 223, 1994, p. 59-111. | Numdam | MR | Zbl

[Fon94b] J.-M. Fontaine, Représentations $p$ -adiques semi-stables, Périodes $p$ -adiques, Séminaire de Bures, 1988, Astérisque 223, 1994, p. 113-183. | MR | Zbl

[Gro72] A. Grothendieck - Groupes de monodromie en géométrie algébrique (SGA7) I, Lecture Notes in Math. 288, Springer, 1972. | MR

[HK94] O. Hyodo &, K. Kato - Semi-stable reduction and crystalline cohomology with logarithmic poles, Périodes $p$ -adiques, Séminaire de Bures, 1988, Astérisque 223, 1994, p. 221-268. | Numdam | MR | Zbl

[Hyo88] O. Hyodo - A note on $p$ -adic etale cohomology in the semi-stable reduction case, Invent math. 91 (1988), p. 543-557. | DOI | EuDML | MR | Zbl

[Hyo91] O. Hyodo, On the de Rham-Witt complex attached to a semi-stable family, Composite Mathematica 78 (1991), p. 241-260. | EuDML | Numdam | MR | Zbl

[Ill90] L. Illusie - Cohomologie de de Rham et cohomologie étale $p$ -adique, Séminaire Bourbaki 1989/90, Exp. 726, Astérisque 189-190, 1990, p. 325-374. | EuDML | Numdam | MR | Zbl

[Jan89] U. Jannsen - On the $ℓ$ -adic cohomology of varieties over number fields and its Galois cohomology, Galois groups over $ℚ$ , Springer, 1989, p. 315-360. | DOI | MR | Zbl

[Kat87] K. Kato - On $p$ -adic vanishing cycles (Application of ideas of Fontaine-Messing), Advanced Studies in Pure Math. 10, 1987, p. 207-251. | DOI | MR | Zbl

[Kat89] K. Kato, Logarithmic structures of Fontaine-Illusie, Algebraic analysis, geometry, and number theory, Johns Hopkins University Press, Baltimore, 1989, p. 191-224. | MR | Zbl

[Kat94a] K. Kato, Semi-stable reduction and $p$ -adic etale cohomology, Périodes $p$ -adiques, Séminaire de Bures, 1988, Astérisque 223, 1994, p. 269-293. | Numdam | MR | Zbl

[Kat94b] K. Kato, Toric singularities, Amer. J. Math. 116 (1994), p. 1073-1099. | DOI | MR | Zbl

[KM92] K. Kato & W. Messing - Syntomic cohomology and $p$ -adic étale cohomology, Tôhoku Math. J. 44 (1992), p. 1-9. | DOI | MR | Zbl

[Kur87] M. Kurihara - A note on $p$ -adic cohomology, Proc. Japan. Academy 63 (1987), p. 275-278. | DOI | MR | Zbl

[Niz98a] W. Niziol - Crystalline conjecture via $K$ -theory, Ann. Scient. E. N. S. 31 (1998), p. 659-681. | EuDML | Numdam | MR | Zbl

[Niz98b] W. Niziol, Semi-stable conjecture for vertical log-smooth families, 1998, preprint.

[Ser67] J.-P. Serre - Sur les groupes de Galois attachés aux groupes $p$ -divisibles, Proc. of a Conf. on local fields, Driebergen 1966, Springer, 1967, p. 118-131. | MR | Zbl

[Tat67] J. Tate - $p$ -divisible groups, Proc. of a Conf. on local fields, Driebergen 1966, Springer, 1967, p. 158-183. | MR | Zbl

[Tsu96] T. Tsuji - Syntomic complexes and $p$ -adic vanishing cycles, J. reine angew. Math. 472 (1996), p. 69-138. | EuDML | MR | Zbl

[Tsu98] T. Tsuji - $p$ -adic Hodge theory in the semi-stable reduction case, Proceedings of the ICM, Vol. II (Berlin, 1998), Doc. Math., 1998, p. 207-216. | EuDML | MR | Zbl

[Tsu99] T. Tsuji - $p$ -adic étale cohomology and crystalline cohomology in the semi-stable reduction case, Invent math 137 (1999), p. 233-411. | DOI | MR | Zbl