Quantization of Hitchin integrable system via positive characteristic

Abstract

In a celebrated unpublished manuscript Beilinson and Drinfeld quantize the Hitchin integrable system by showing that the global sections of critically twisted differential operators on the moduli stack of G-bundles on an algebraic curve is identified with the ring of regular functions on the space of G-opers; they deduce existence of an automorphic D-module corresponding to a local system carrying a structure of an oper. In this note we show for G=GL(n) that those results admit a short proof by reduction to positive characteristic, where the result is deduced from generic Langlands duality established earlier by the first author and A. Braverman. The appendix contains a proof of some properties of the p-curvature map restricted to the space of opers.Comment: paper by Roman Bezrukavnikov and Roman Travkin with an appendix by Roman Bezrukavnikov, Tsao-Hsien Chen and Xinwen Zhu. 13 page