Finiteness of crystalline cohomology of higher level
[Finitude de la cohomologie cristalline de niveau fini]
Miyatani, Kazuaki
Annales de l'Institut Fourier, Tome 65 (2015), p. 975-1004 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

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.

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/aif.2949
Classification:  14F30
Mots clés: cohomologie cristalline de niveau fini, lemme de Poincaré 
@article{AIF_2015__65_3_975_0,
     author = {Miyatani, Kazuaki},
     title = {Finiteness of crystalline cohomology of higher level},
     journal = {Annales de l'Institut Fourier},
     volume = {65},
     year = {2015},
     pages = {975-1004},
     doi = {10.5802/aif.2949},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2015__65_3_975_0}
}

Miyatani, Kazuaki. Finiteness of crystalline cohomology of higher level. Annales de l'Institut Fourier, Tome 65 (2015) pp. 975-1004. doi : 10.5802/aif.2949. http://gdmltest.u-ga.fr/item/AIF_2015__65_3_975_0/

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

[2] Berthelot, Pierre Cohomologie cristalline des schémas de caractéristique p > 0 , Springer-Verlag, Berlin-New York, Lecture Notes in Mathematics, Vol. 407 (1974), pp. 604 | MR 384804 | Zbl 0298.14012

[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), Tome 29 (1996) no. 2, pp. 185-272 | Numdam | MR 1373933 | Zbl 0886.14004

[5] Berthelot, Pierre 𝒟-modules arithmétiques. II. Descente par Frobenius, Mém. Soc. Math. Fr. (N.S.) (2000) no. 81, pp. vi+136 | Numdam | Zbl 0948.14017

[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, Springer-Verlag, Lecture Notes in Math., Tome 225 (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 491705 | Zbl 0383.14010

[9] Le Stum, Bernard; Quirós, Adolfo Transversal crystals of finite level, Ann. Inst. Fourier (Grenoble), Tome 47 (1997) no. 1, pp. 69-100 | Article | Numdam | MR 1437179 | Zbl 0883.14006

[10] Le Stum, Bernard; Quirós, Adolfo The exact Poincaré lemma in crystalline cohomology of higher level, J. Algebra, Tome 240 (2001) no. 2, pp. 559-588 | Article | MR 1841347 | Zbl 1064.14015