Journal of the Ramanujan Mathematical Society

Volume 28A, Issue SPL, July – Special Issue 2013 pp. 123–147.

Geometric Langlands correspondence near opers

Authors: Edward Frenkel and Constantin Teleman
Author institution: Department of Mathematics, University of California, Berkeley, CA 94720, USA

Summary: Let G be a complex, connected semi-simple Lie group, LG its Langlands dual group, BunG the moduli stack of G-bundles on a smooth projective curve Σ over C, LocLG the moduli stack of flat LG-bundles} on Σ. Beilinson and Drinfeld have constructed an equivalence between the category of coherent sheaves on LG supported scheme-theoretically at the locus of opers and the category of D-modles on BunG admitting a certain global presentation. We generalize it to an equivalence between the derived category of coherent sheaves on LocLG supported at the formal neighborhood of the locus of opers and the localization at D of the derived category of D-modules on BunG (and an appropriate equivalence of abelian categories).

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