Geometric Arthur Parameters

Abstract

We study unramified principal Eisenstein series from the perspective of the geometric Lang- lands equivalence. We prove a geometrization of the Langlands constant term formula and show that it recovers the classical result after applying the categorical trace of Frobenius. By analyzing the singular support filtration on the category of ind-coherent sheaves on the stack of local systems with restricted variation, we produce a generalization of a formula of D. Kazhdan and A. Okounkov. As a result we produce an upper bound on the spectrum of the Hecke algebra associated to a rational point of a curve, relative to its action on unramified principal Eisenstein series.