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Géométrie algébrique
The connectedness of degeneracy loci in positive characteristic
Rémi Lodh1
1 Springer-Verlag, Tiergartenstr. 17, 69121 Heidelberg, Germany
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 959-964.

A well-known result of Fulton–Lazarsfeld ensures the connectedness of degeneracy loci under an ampleness condition. We extend it to positive characteristic, along with the variants for degeneracy loci of symmetric and alternating maps of even rank, due to Tu in characteristic zero. The proof uses the explicit determination of the top étale cohomology group of an algebraic variety, a result communicated by Esnault.

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DOI : 10.5802/crmath.448
Classification : 14F20, 14N05, 14J60, 14F06, 14M12, 14F45, 14E15, 14G17

Rémi Lodh 1

1 Springer-Verlag, Tiergartenstr. 17, 69121 Heidelberg, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Rémi Lodh. The connectedness of degeneracy loci in positive characteristic. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 959-964. doi : 10.5802/crmath.448. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.448/

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