Number of cuspidal automorphic representations and Hitchin's moduli spaces
Abstract
Let F be the function field of a projective smooth geometrically connected curve X defined over a finite field. Let G be a split semisimple reductive group over X. We express the sum of cuspidal multiplicities of G automorphic representations with fixed regular depth zero local behaviours as in terms of cardinality of F_qpoints of Hitchin's moduli spaces of groups associated to G. We also consider the case G=GL_n where we refine the results and verify Deligne's conjecture on counting irreducible $\ell$adic local systems with of tame regular generic local monodromies.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.13858
 Bibcode:
 2021arXiv211013858Y
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Representation Theory
 EPrint:
 78 pages