Independence of ell of Monodromy Groups
| dc.creator | Chin, CheeWhye | |
| dc.date | 2002-06-14 | |
| dc.date | 2004-07-31 | |
| dc.date.accessioned | 2026-07-07T04:49:07Z | |
| dc.date.available | 2026-07-07T04:49:07Z | |
| dc.description | Let X be a smooth curve over a finite field of characteristic p, let E be a number field, and consider an E-compatible system of lisse sheaves on the curve X. For each place lambda of E not lying over p, the lambda-component of the system is a lisse E_lambda-sheaf on X, whose associated arithmetic monodromy group is an algebraic group over the local field E_lambda. We use Serre's theory of Frobenius tori and Lafforgue's proof of Deligne's conjecture to show that when the E-compatible system is semisimple and pure of some integer weight, the isomorphism type of the identity component of these monodromy groups is ``independent of lambda''. More precisely: after replacing E by a finite extension, there exists a connected split reductive algebraic group G_0 over the number field E such that for every place lambda of E not lying over p, the identity component of the arithmetic monodromy group of the lambda-component of the system is isomorphic to the group G_0 with coefficients extended to the local field E_lambda. | |
| dc.description | 25 pages, AMS-LaTeX; journal version | |
| dc.identifier | https://arxiv.org/abs/math/0206147 | |
| dc.identifier | http://arxiv.org/abs/math/0206147 | |
| dc.identifier | J. Amer. Math. Soc. 17 (2004), no.3, 723--747 | |
| dc.identifier | doi:10.1090/S0894-0347-04-00456-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64305 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G10 (11G40 14F20) | |
| dc.title | Independence of ell of Monodromy Groups | |
| dc.type | text |