TY - JOUR

T1 - Local-to-global extensions for GLn in non-zero characteristic

T2 - A characterization of γf(s, π, Sym2, Ψ) and γf(s, π, ∇2, Ψ)

AU - Henniart, Guy

AU - LOMELÍ , LUIS ALBERTO

PY - 2011/2/1

Y1 - 2011/2/1

N2 - Let F be a locally compact field of positive characteristic. In his thesis, the second author used the Langlands-Shahidi method to define γ-factors for the symmetric square and exterior square representations of the dual group of GLn(F). We prove here that such γ-factors are characterized by local properties - including a multiplicativity property with respect to parabolic induction - and their role in global functional equations for L-functions. For this, we prove that a given cuspidal representation of GL n(F) is the component at some place of a global automorphic representation, the ramification of which is controlled at other places. In fact, we use an equivalent result for l-adic Galois representations, due to O. Gabber and N. Katz, and transport it via the global Langlands correspondence proved by L. Lafforgue.

AB - Let F be a locally compact field of positive characteristic. In his thesis, the second author used the Langlands-Shahidi method to define γ-factors for the symmetric square and exterior square representations of the dual group of GLn(F). We prove here that such γ-factors are characterized by local properties - including a multiplicativity property with respect to parabolic induction - and their role in global functional equations for L-functions. For this, we prove that a given cuspidal representation of GL n(F) is the component at some place of a global automorphic representation, the ramification of which is controlled at other places. In fact, we use an equivalent result for l-adic Galois representations, due to O. Gabber and N. Katz, and transport it via the global Langlands correspondence proved by L. Lafforgue.

UR - http://www.scopus.com/inward/record.url?scp=79251572107&partnerID=8YFLogxK

U2 - 10.1353/ajm.2011.0006

DO - 10.1353/ajm.2011.0006

M3 - Article

AN - SCOPUS:79251572107

VL - 133

SP - 187

EP - 196

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

IS - 1

ER -