Independence of l in Lafforgue's theorem
| dc.creator | Chin, CheeWhye | |
| dc.date | 2002-06-02 | |
| dc.date | 2002-06-25 | |
| dc.date.accessioned | 2026-07-07T04:48:50Z | |
| dc.date.available | 2026-07-07T04:48:50Z | |
| dc.description | Let X be a smooth curve over a finite field of characteristic p, let l be a prime number different from p, and let L be an irreducible lisse l-adic sheaf on X whose determinant is of finite order. By a theorem of Lafforgue, for each prime number l' different from p, there exists an irreducible lisse l'-adic sheaf L' on X which is compatible with L, in the sense that at every closed point x of X, the characteristic polynomials of Frobenius at x for L and L' are equal. We prove an "independence of l" assertion on the fields of definition of these irreducible l'-adic sheaves L' : namely, that there exists a number field F such that for any prime number l' different from p, the l'-adic sheaf L' above is defined over the completion of F at one of its l'-adic places. | |
| dc.description | 19 pages, AMSTeX; revised version 2 to appear in Advances in Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0206001 | |
| dc.identifier | http://arxiv.org/abs/math/0206001 | |
| dc.identifier | Adv. Math. 180 (2003), no. 1, 64--86 | |
| dc.identifier | doi:10.1016/S0001-8708(02)00082-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64201 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G10 (14F20 14G13 14G15) | |
| dc.title | Independence of l in Lafforgue's theorem | |
| dc.type | text |