Hodge type of the exotic cohomology of complete intersections

Hélène Esnault; Daqing Wan

doi:10.1016/S1631-073X(03)00013-X

Algebraic Geometry

Hodge type of the exotic cohomology of complete intersections
[Type de Hodge de la cohomologie exotique des intersections complètes]

Présenté par : Pierre Deligne

Hélène Esnault ¹ ; Daqing Wan ²

¹ Mathematik, Universität Essen, FB 6, Mathematik, 45117 Essen, Germany
² Department of Mathematics, University of California, Irvine, CA 92697-3875, USA

Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 153-157.

Résumé
Abstract

Si $X \subset ℙ^{n}$ est une intersection complète lisse, sa cohomologie modulo celle de $ℙ^{n}$ est supportée en dimension moitié. Si l'intersection complète est singulière, elle peut aussi avoir de la cohomologie exotique en dimension supérieure. Nous montrons qu' on peut améliorer le type de Hodge de cette cohomologie de de Rham exotique.

If $X \subset ℙ^{n}$ is a smooth complete intersection, its cohomology modulo the one of $ℙ^{n}$ is supported in middle dimension. If the complete intersection is singular, it might also carry exotic cohomology beyond the middle dimension. We show that for this exotic cohomology, one can improve the known bound for the Hodge type of its de Rham cohomology.

Reçu le : 2002-12-10
Accepté le : 2002-12-16
Publié le : 2003-01-15

DOI : 10.1016/S1631-073X(03)00013-X

Affiliations des auteurs :

Hélène Esnault ¹ ; Daqing Wan ²

¹ Mathematik, Universität Essen, FB 6, Mathematik, 45117 Essen, Germany
² Department of Mathematics, University of California, Irvine, CA 92697-3875, USA

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Hélène Esnault; Daqing Wan. Hodge type of the exotic cohomology of complete intersections. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 153-157. doi : 10.1016/S1631-073X(03)00013-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00013-X/

Bibliographie
Cité par

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Hélène Esnault; Daqing Wan Divisibility of Frobenius eigenvalues on $ℓ$ -adic cohomology, Proceedings of the Indian Academy of Sciences. Mathematical Sciences, Volume 132 (2022) no. 2, p. 7 (Id/No 60) | DOI:10.1007/s12044-022-00697-0 | Zbl:1499.14040
Luc Illusie Miscellany on traces in $ℓ$ -adic cohomology: a survey, Japanese Journal of Mathematics. 3rd Series, Volume 1 (2006) no. 1, pp. 107-136 | DOI:10.1007/s11537-006-0504-3 | Zbl:1156.14309

Cité par 2 documents. Sources : zbMATH

^☆ The first author is supported by the DFG-Schwerpunkt “Komplexe Mannigfaltigkeiten” while the second author is partially supported by the NSF.

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