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Article de recherche - Géométrie algébrique, Théorie des nombres
Some remarks on the companions conjecture for normal varieties
Marco D’Addezio1
1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, SU - 4 place Jussieu, Case 247, 75005 Paris
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 63-69.

Drinfeld in 2010 proved the companions conjecture for smooth varieties over a finite field, generalizing L. Lafforgue’s result for smooth curves. We study the obstruction to prove the conjecture for arbitrary normal varieties. To do this, we introduce a new property of morphisms. We verify this property in some cases, showing thereby the companions conjecture for some singular normal varieties.

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DOI : 10.5802/crmath.527
Classification : 14G15
Mots clés : $\ell $-adic representation, independence of $\ell $, étale fundamental group
Marco D’Addezio 1

1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, SU - 4 place Jussieu, Case 247, 75005 Paris
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Some remarks on the companions conjecture for normal varieties},
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Marco D’Addezio. Some remarks on the companions conjecture for normal varieties. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 63-69. doi : 10.5802/crmath.527. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.527/

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