Independence of l in Lafforgue's theorem

dc.creatorChin, CheeWhye
dc.date2002-06-02
dc.date2002-06-25
dc.date.accessioned2026-07-07T04:48:50Z
dc.date.available2026-07-07T04:48:50Z
dc.descriptionLet 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.description19 pages, AMSTeX; revised version 2 to appear in Advances in Mathematics
dc.identifierhttps://arxiv.org/abs/math/0206001
dc.identifierhttp://arxiv.org/abs/math/0206001
dc.identifierAdv. Math. 180 (2003), no. 1, 64--86
dc.identifierdoi:10.1016/S0001-8708(02)00082-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64201
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14G10 (14F20 14G13 14G15)
dc.titleIndependence of l in Lafforgue's theorem
dc.typetext

Files

Collections