Local cohomology multiplicities in terms of étale cohomology

Blickle, Manuel; Bondu, Raphaël

doi:10.5802/aif.2160

Local cohomology multiplicities in terms of étale cohomology
[Multiplicités de la cohomologie locale en termes de cohomologie étale]

Blickle, Manuel ¹ ; Bondu, Raphaël ²

¹ Universität Essen, FB6 Mathematik, 45117 Essen (Allemagne)
² 9 rue des Ternes, 75017 Paris (France)

Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2239-2256.

Résumé
Abstract

En utilisant la correspondance récemment introduite par Emerton et Kisin, nous donnons une description des invariants de cohomologie locale de Lyubeznik en termes de cohomologie locale étale à coefficients dans $𝐙 / p 𝐙$ .

Using a recently introduced correspondence of Emerton-Kisin we give a description of Lyubeznik’s local cohomology invariants in terms of local étale cohomology with $𝐙 / p 𝐙$ coefficients.

EuDML MR Zbl

DOI : 10.5802/aif.2160

Classification : 14B15, 14F20
Keywords: Local cohomology, characteristic

p

, perverse sheaves, Local cohomology, characteristic

p

, perverse sheaves
Mot clés : cohomologie locale, caractéristique

p

, faisceaux pervers

Affiliations des auteurs :

Blickle, Manuel ¹ ; Bondu, Raphaël ²

¹ Universität Essen, FB6 Mathematik, 45117 Essen (Allemagne)
² 9 rue des Ternes, 75017 Paris (France)

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     author = {Blickle, Manuel and Bondu, Rapha\"el},
     title = {Local cohomology multiplicities in terms of \'etale cohomology},
     journal = {Annales de l'Institut Fourier},
     pages = {2239--2256},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {55},
     number = {7},
     year = {2005},
     doi = {10.5802/aif.2160},
     mrnumber = {2207383},
     zbl = {1092.14005},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.2160/}
}

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Blickle, Manuel; Bondu, Raphaël. Local cohomology multiplicities in terms of étale cohomology. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2239-2256. doi : 10.5802/aif.2160. https://www.numdam.org/articles/10.5802/aif.2160/

Bibliographie
Cité par

[BK81] Brylinski, J.-L.; Kashiwara, M. Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math., Volume 64 (1981) no. 3, pp. 387-410 | DOI | EuDML | MR | Zbl

[Bli01] Blickle, M. The intersection homology $D$ -module in positive characteristic, 2001 (Univ. of Michigan Dissertation)

[Bli04] Blickle, M. The intersection homology $D$ -module in finite characteristic, Math. Ann., Volume 328 (2004), pp. 425-450 | DOI | MR | Zbl

[Bor84] al, A. Borel| et Intersection cohomology, Progress in Mathematics, 50, Birkhäuser Boston Inc., Boston, MA, 1984 (Notes on the seminar held at the University of Bern, Bern, 1983, Swiss Seminars) | Zbl

[EK03] Emerton, M.; Kisin, M. An introduction to the Riemann-Hilbert correspondence for unit $ℱ$ -crystals., Geometric aspects of Dwork theory, Volume I, II, Walter de Gruyter GmbH & Co. KG, Berlin, 2004, pp. 677-700 | MR | Zbl

[EK04] Emerton, M.; Kisin, M. Riemann-Hilbert correspondence for unit $ℱ$ -crystals., Astérisque (2004) no. 293, pp. vi+257 | Numdam | MR | Zbl

[Gab00] Gabber, O. Notes on some $t$ -structures (2000) (handwritten notes)

[GLS98] GarcÍa, R.; López; Sabbah, C. Topological computation of local cohomology multiplicities, Collect. Math., Volume 49 (1998) no. 2-3, pp. 317-324 (Dedicated to the memory of Fernando Serrano) | EuDML | MR | Zbl

[HS77] Hartshorne, R.; Speiser, R. Local cohomological dimension in characteristic $p$ , Annals of Mathematics, Volume 105 (1977), pp. 45-79 | DOI | MR | Zbl

[HS93] Huneke, C.L.; Sharp, Ro.Y. Bass numbers of local cohomology modules, Trans. Amer. Math. Soc., Volume 339 (1993) no. 2, pp. 765-779 | DOI | MR | Zbl

[Hun96] Huneke, C. Tight closure and its applications (1996) (Conference Board of the Mathematical Sciences, With an appendix by Melvin Hochster) | MR | Zbl

[KS90] Kashiwara, M.; Schapira, P. Sheaves on manifolds, Grundlehren der mathematischen Wissenschaften, 292, Springer-Verlag, 1990 | MR | Zbl

[KW01] Kiehl, R.; Weissauer, R. Weil conjectures, perverse sheaves and $l$ 'adic Fourier transform, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 42, Springer-Verlag, Berlin, 2001 | MR | Zbl

[Lyu93] Lyubeznik, G. Finiteness properties of local cohomology modules (an application of $D$ -modules to commutative algebra), Invent. Math., Volume 113 (1993) no. 1, pp. 41-55 | DOI | EuDML | MR | Zbl

[Lyu97] Lyubeznik, G. $ℱ$ -modules: an application to local cohomology and $D$ -modules in characteristic $p > 0$ , Journal für reine und angewandte Mathematik, Volume 491 (1997), pp. 65-130 | DOI | MR | Zbl

[Mas] Massey, D. B. Intersection Cohomology, Monodromy, and the Milnor Fiber | Zbl

[Mil80] Milne, J. S. Étale cohomology, Princeton University Press, Princeton, New Jersey, 1980 | MR | Zbl

[Ogu73] Ogus, A. Local cohomological dimension of algebraic varieties, Ann. of Math., Volume 98 (1973) no. 2, pp. 327-365 | DOI | MR | Zbl

[Tor] Torrelli, T. Intersection homology D-module and Bernstein polynomials associated with a complete intersection (2004) (preprint) | Zbl

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