Scholze and Shin [J. Amer. Math. Soc. 26 (2013), pp. 261–294] gave a conjectural formula relating the traces on automorphic Galois sides of local Langlands correspondence. Their work generalized an earlier Scholze, which he used to give new proof conjecture for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper G normal L S...

Abstract Kottwitz’s conjecture describes the contribution of a supercuspidal representation to cohomology local Shimura variety in terms Langlands correspondence. A natural extension this concerns Scholze’s more general spaces shtukas. Using new Lefschetz–Verdier trace formula for v-stacks, we prove extended conjecture, disregarding action Weil group, and modulo virtual whose character vanishes...

If ρ is a selfdual representation of a group G on a vector space V over C, we will say that ρ is orthogonal, resp. symplectic, if G leaves a nondegenerate symmetric, resp. alternating, bilinear form B : V ×V → C invariant. If ρ is irreducible, exactly one of these possibilities will occur, and we may define a sign c(ρ) ∈ {±1}, taken to be +1, resp. −1, in the orthogonal, resp. symplectic, case....

The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, asked whether it possible to construct a function-theoretic version. In this paper we use the algebra commuting global differential operators (quantum Hitchin Hamiltonians and their conjugates) on moduli space <mml:math xmln...