On a vanishing conjecture appearing in the geometric Langlands correspondence

الأصل · EN

Let X be a smooth complete curve, and let Bunₙ 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 Avₑᵈ acting from the category D(Bunₙ) 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.