A coarse geometric expansion of a variant of Arthur's truncated traces and some applications

Abstract

Let F be a global function field with constant field ${\mathbb{F}}_q$. Let G be a reductive group over ${\mathbb{F}}_q$. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation. As applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line ${\mathbb{P}}_{{\mathbb{F}}_q}^1$ with two points of ramifications.

38 pages, minor revision

References in corpus (1)

• Nilpotent orbits over ground fields of good characteristic

Cited by in corpus (1)

• Rank 2 $\ell$-adic local systems and Higgs bundles over a curve