Year: 2012
Type: article
Abstract: A brief survey is given of the classical Langlands correspondence between n-dimensional representations of Galois groups of local and global fields of dimension 1 and irreducible representations of the groups GL(n). A generalization of the Langlands program to fields of dimension 2 is considered and the corresponding version for 1-dimensional representations is described. We formulate a conjecture on a direct image (=automorphic induction) of automorphic forms which links the Langlands correspondences in dimension 2 and 1. The direct image conjecture implies the classical Hasse-Weil conjecture on the analytical behaviour of the L-functions of curves defined over global fields of dimension 1.
Source: Russian Mathematical Surveys
Author: Aleksei N Parshin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1998551619