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My apologies for the imprecise question(s), it should be clear enough that I´m a complete beginner in this subject. The (de Rham) Geometric Langlands Conjecture over $\mathbb{C}$ takes as input a ...

I'm currently working through Frenkel's beautiful paper: http://arxiv.org/PS_cache/hep-th/pdf/0512/0512172v1.pdf. I'm looking for a good example of a projective curve to get my hands dirty, and go ...

Given a curve C, and a reductive group G, there is a moduli stack Loc_G(C), the stack of G-local systems. I keep reading that there's a substack of "opers" but am having trouble locating a definition....