Quantization of Hitchin integrable system via positive characteristic

The main result of the seminal (unpublished) work of Beilinson-Drinfeld is the construction of an automorphic sheaf corresponding to a local system which carries the additional structure of an oper. This is achieved by quantizing the Hitchin integrable system. In this note we show (in the case of G = GL(n)) that this result admits a short proof based on positive characteristic methods. In the appendix we study the restriction of the p-curvature (pHitchin) map to the space of opers, we8Ul5tAYGy7kxpCMuQTTXbDj5RqBshow it is finite and flat by checking it is asymptotic to Frobenius at infinity. We speculate on the relation of this result to a conjecture of Frenkel, Etingof and Kazhdan on the spectrum of global critically twisted differential operators on Bun_G acting on the space of L² sections of the bundle of half forms.