Some remarks on the companions conjecture for normal varieties

Marco D’Addezio

doi:10.5802/crmath.527

Research article - Algebraic geometry, Number theory

Some remarks on the companions conjecture for normal varieties

Marco D’Addezio ¹

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

Abstract

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.

Received: 2022-06-27
Revised: 2023-04-16
Accepted: 2023-06-15
Published online: 2024-02-02

DOI: 10.5802/crmath.527

Classification: 14G15
Keywords: $\ell $-adic representation, independence of $\ell $, étale fundamental group

Author's affiliations:

Marco D’Addezio ¹

¹ Institut de Mathématiques de Jussieu-Paris Rive Gauche, SU - 4 place Jussieu, Case 247, 75005 Paris

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Marco D{\textquoteright}Addezio},
     title = {Some remarks on the companions conjecture for normal varieties},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {63--69},
     year = {2024},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     doi = {10.5802/crmath.527},
     language = {en},
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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

References
Cited by

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