Finiteness of crystalline cohomology of higher level
Annales de l'Institut Fourier, Volume 65 (2015) no. 3, pp. 975-1004.

We prove the finiteness of crystalline cohomology of higher level. An important ingredient is a “higher de Rham complex” that satisfies a kind of Poincaré lemma.

Nous prouvons la finitude de la cohomologie cristalline de niveau fini. Un ingrédient important est un “complexe de de Rham supérieur” qui satisfait un analogue du lemme de Poincaré.

DOI: 10.5802/aif.2949
Classification: 14F30
Keywords: crystalline cohomology of higher level, Poincaré lemma
Mot clés : cohomologie cristalline de niveau fini, lemme de Poincaré
Miyatani, Kazuaki 1

1 National Center for Theoretical Sciences, Mathematics Division (Taipei Office), National Taiwan University, Taipei 10617 (Taiwan)
@article{AIF_2015__65_3_975_0,
     author = {Miyatani, Kazuaki},
     title = {Finiteness of crystalline cohomology of higher level},
     journal = {Annales de l'Institut Fourier},
     pages = {975--1004},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {65},
     number = {3},
     year = {2015},
     doi = {10.5802/aif.2949},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2949/}
}
TY  - JOUR
AU  - Miyatani, Kazuaki
TI  - Finiteness of crystalline cohomology of higher level
JO  - Annales de l'Institut Fourier
PY  - 2015
SP  - 975
EP  - 1004
VL  - 65
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.2949/
DO  - 10.5802/aif.2949
LA  - en
ID  - AIF_2015__65_3_975_0
ER  - 
%0 Journal Article
%A Miyatani, Kazuaki
%T Finiteness of crystalline cohomology of higher level
%J Annales de l'Institut Fourier
%D 2015
%P 975-1004
%V 65
%N 3
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.2949/
%R 10.5802/aif.2949
%G en
%F AIF_2015__65_3_975_0
Miyatani, Kazuaki. Finiteness of crystalline cohomology of higher level. Annales de l'Institut Fourier, Volume 65 (2015) no. 3, pp. 975-1004. doi : 10.5802/aif.2949. http://archive.numdam.org/articles/10.5802/aif.2949/

[1] Artin, Michael; Grothendieck, Alexander; Verdier, Jean-Louis Théorie de Topos et Cohomologie Étale des Schémas I, II, III, Lecture Notes in Math., 269, 270, 305, Springer-Verlag, 1971

[2] Berthelot, Pierre Cohomologie cristalline des schémas de caractéristique p > 0 , Lecture Notes in Mathematics, Vol. 407, Springer-Verlag, Berlin-New York, 1974, pp. 604 | MR | Zbl

[3] Berthelot, Pierre Letter to Illusie, 1990

[4] Berthelot, Pierre 𝒟-modules arithmétiques. I. Opérateurs différentiels de niveau fini, Ann. Sci. École Norm. Sup. (4), Volume 29 (1996) no. 2, pp. 185-272 | Numdam | MR | Zbl

[5] Berthelot, Pierre 𝒟-modules arithmétiques. II. Descente par Frobenius, Mém. Soc. Math. Fr. (N.S.) (2000) no. 81, pp. vi+136 | Numdam | Zbl

[6] Berthelot, Pierre Letter to Abe and the author, 2010

[7] Berthelot, Pierre; Grothendieck, Alexander; Illusie, Luc Théorie des Intersections et Théorème de Riemann-Roch, Lecture Notes in Math., 225, Springer-Verlag, 1971

[8] Berthelot, Pierre; Ogus, Arthur Notes on crystalline cohomology, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1978, pp. vi+243 | MR | Zbl

[9] Le Stum, Bernard; Quirós, Adolfo Transversal crystals of finite level, Ann. Inst. Fourier (Grenoble), Volume 47 (1997) no. 1, pp. 69-100 | DOI | Numdam | MR | Zbl

[10] Le Stum, Bernard; Quirós, Adolfo The exact Poincaré lemma in crystalline cohomology of higher level, J. Algebra, Volume 240 (2001) no. 2, pp. 559-588 | DOI | MR | Zbl

Cited by Sources: