Some remarks on the companions conjecture for normal varieties
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 prop...
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| Language: | English |
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Académie des sciences
2024-02-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.527/ |
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| author | D’Addezio, Marco |
| author_facet | D’Addezio, Marco |
| author_sort | D’Addezio, Marco |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2f083231ae47406a9892303a9dbb9fe5 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-2f083231ae47406a9892303a9dbb9fe52025-02-07T11:12:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-02-01362G1636910.5802/crmath.52710.5802/crmath.527Some remarks on the companions conjecture for normal varietiesD’Addezio, Marco0Institut de Mathématiques de Jussieu-Paris Rive Gauche, SU - 4 place Jussieu, Case 247, 75005 ParisDrinfeld 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.527/$\ell $-adic representationindependence of $\ell $étale fundamental group |
| spellingShingle | D’Addezio, Marco Some remarks on the companions conjecture for normal varieties Comptes Rendus. Mathématique $\ell $-adic representation independence of $\ell $ étale fundamental group |
| title | Some remarks on the companions conjecture for normal varieties |
| title_full | Some remarks on the companions conjecture for normal varieties |
| title_fullStr | Some remarks on the companions conjecture for normal varieties |
| title_full_unstemmed | Some remarks on the companions conjecture for normal varieties |
| title_short | Some remarks on the companions conjecture for normal varieties |
| title_sort | some remarks on the companions conjecture for normal varieties |
| topic | $\ell $-adic representation independence of $\ell $ étale fundamental group |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.527/ |
| work_keys_str_mv | AT daddeziomarco someremarksonthecompanionsconjecturefornormalvarieties |