2002/06/25 by CheeWhye Chin · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #advanced mathematical theories #math.AG #math.NT #msc:14G10 #msc:14G13
paper · pdf · doi:10.1016/s0001-8708(02)00082-8
published as Adv. Math. 180 (2003), no. 1, 64--86 · 19 pages, AMSTeX; revised version 2 to appear in Advances in Mathematics
arxiv created 2002/06/25 · openalex publication_date 2003/02/17 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.