The image of the constant sheaf under the geometric Langlands equivalence

Abstract

Let $X$ be a smooth projective curve and let $G$ be a reductive group over an algebraically closed field of characteristic zero. We compute the image of arbitrary finite-rank local systems on ${\mathrm{Bun}}_G(X)$ under the geometric Langlands equivalence, confirming a conjecture of V. Lafforgue in the case of the constant sheaf.

arXiv comment20 pages