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On a vanishing conjecture appearing in the geometric Langlands correspondence

D. Gaitsgory
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Abstract

Let $X$ be a smooth complete curve, and let $Bun_n$ be the moduli stack of rank $n$ vector bundles on $X$. Let $E$ be a local system on $X$. In a recent paper of E.Frenkel, K.Vilonen and the author, it was shown that the vanishing of a certian functor $Av_E^d$ acting from the category $D(Bun_n)$ to itself, implies the geometric Langlands conjecture. In this paper we establish the required vanishing result. Our proof works for sheaves with char=0 coefficients, or with torsion coefficients when the parameter $d$ is less than the characteristic.

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D. Gaitsgory. 2003-10-24. On a vanishing conjecture appearing in the geometric Langlands correspondence. https://arxiv.org/abs/math/0204081

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