Duke Mathematical Journal

Cohomologie Étale de $p$-torsion et cohomologie cristalline en réduction semi-stable

Christophe Breuil

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 95, Number 3 (1998), 523-620.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077229890

Mathematical Reviews number (MathSciNet)
MR1658764

Zentralblatt MATH identifier
0961.14010

Digital Object Identifier
doi:10.1215/S0012-7094-98-09514-X

Subjects
Primary: 14F30: $p$-adic cohomology, crystalline cohomology
Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10] 14G20: Local ground fields

Citation

Breuil, Christophe. Cohomologie Étale de p -torsion et cohomologie cristalline en réduction semi-stable. Duke Mathematical Journal 95 (1998), no. 3, 523--620. doi:10.1215/S0012-7094-98-09514-X. http://projecteuclid.org/euclid.dmj/1077229890.


Export citation

References

  • [Be] P. Berthelot, Cohomologie cristalline des schémas de caractéristique $p>0$, Lecture Notes in Math., vol. 407, Springer-Verlag, Berlin, 1974.
  • [BO1] P. Berthelot and A. Ogus, Notes on crystalline cohomology, Princeton Univ. Press, Princeton, N.J., 1978.
  • [BO2] P. Berthelot and A. Ogus, $F$-isocrystals and de Rham cohomology, I, Invent. Math. 72 (1983), no. 2, 159–199.
  • [Br1] C. Breuil, Topologie log-syntomique, cohomologie log-cristalline et cohomologie de Čech, Bull. Soc. Math. France 124 (1996), no. 4, 587–647.
  • [Br2] C. Breuil, Représentations $p$-adiques semi-stables et transversalité de Griffiths, Math. Ann. 307 (1997), no. 2, 191–224.
  • [Br3] C. Breuil, Construction de représentations $p$-adiques semi-stables, Ann. Sci. École Norm. Sup. (4) 31 (1998), no. 3, 281–327.
  • [DI] P. Deligne and L. Illusie, Relèvements modulo $p^2$ et décomposition du complexe de de Rham, Invent. Math. 89 (1987), no. 2, 247–270.
  • [ES] J.-Y. Etesse and B. Le Stum, Fonctions $L$ associées aux $F$-isocristaux surconvergents, II: Zéros et pôles unités, Invent. Math. 127 (1997), no. 1, 1–31.
  • [Fa1] G. Faltings, Crystalline cohomology and $p$-adic Galois representations, Algebraic Analysis, Geometry, and Number Theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, Md., 1989, pp. 25–80.
  • [Fa2] G. Faltings, Crystalline cohomology of semistable curves, and $p$-adic Galois representations, J. Algebraic Geom. 1 (1992), no. 1, 61–81.
  • [Fo] J.-M. Fontaine, Le corps des périodes $p$-adiques, Astérisque 223 (1994), 59–111, Péripodes $p$-adiques (Bures-sur-Yvette, 1988), Soc. Math. France, Montrouge.
  • [FL] J.-M. Fontaine and G. Laffaille, Construction de représentations $p$-adiques, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 4, 547–608.
  • [FM] J.-M. Fontaine and W. Messing, $p$-adic periods and $p$-adic étale cohomology, Current Trends in Arithmetical Algebraic Geometry (Arcata, Calif., 1985), Contemp. Math., vol. 67, Amer. Math. Soc., Providence, 1987, pp. 179–207.
  • [Hy] O. Hyodo, A note on $p$-adic étale cohomology in the semistable reduction case, Invent. Math. 91 (1988), no. 3, 543–557.
  • [HK] O. Hyodo and K. Kato, Semi-stable reduction and crystalline cohomology with logarithmic poles, Astérisque 223 (1994), 221–268, Périodes $p$-adiques (Bures-sur-Yvette, 1988), Soc. Math. France, Montrouge.
  • [Il1] L. Illusie, Complexe de de Rham-Witt et cohomologie cristalline, Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 4, 501–661.
  • [Il2] L. Illusie, Cohomologie de de Rham et cohomologie étale $p$-adique (d'après G. Faltings, J.-M. Fontaine et al.), Astérisque 189-190 (1990), no. 726, 325–374, Séminaire Bourbaki, Vol. 1989–90.
  • [Il3] L. Illusie, 8 juin 1996, lettre.
  • [Ka1] K. Kato, On $p$-adic vanishing cycles (application of ideas of Fontaine-Messing), Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 207–251.
  • [Ka2] K. Kato, Logarithmic structures of Fontaine-Illusie, Algebraic Analysis, Geometry, and Number Theory, (Baltimore, Md., 1988), Johns Hopkins Univ. Press, Baltimore, 1989, pp. 191–224.
  • [Ka3] K. Kato, Semi-stable reduction and $p$-adic étale cohomology, Astérisque (1994), no. 223, 269–293, Périodes $p$-adiques (Bures-sur-Yvette, 1988), Soc. Math. France, Montrouge.
  • [KM] K. Kato and W. Messing, Syntomic cohomology and $p$-adic étale cohomology, Tohoku Math. J. (2) 44 (1992), no. 1, 1–9.
  • [Ma] H. Matsumura, Commutative Ring Theory, 2nd ed., Cambridge Stud. Adv. Math., vol. 8, Cambridge Univ. Press, Cambridge, 1989.
  • [Se] J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972), no. 4, 259–331.
  • [Ts1] T. Tsuji, Syntomic complexes and $p$-adic vanishing cycles, J. Reine Angew. Math. 472 (1996), 69–138.
  • [Ts2] T. Tsuji, A note on log-crystalline cohomology and log-syntomic cohomology, preprint, Kyoto, 1994.
  • [Ts3] T. Tsuji, $p$-adic-étale cohomology and crystalline cohomology in the semi- stable reduction case, preprint, Kyoto, 1996.