Holmstrom Geometric Langlands

Check out the MO answers of Ben-Zvi, in particular discussions of how physics should tell us what to look for when generalizing to higher dimensions.

http://www.ncatlab.org/nlab/show/geometric+Langlands

http://mathoverflow.net/questions/4180/consequences-of-geometric-langlands/

Frenkel and Gross: A rigid irregular connection on the projective line http://arxiv.org/abs/0901.2163 Some kind of analogue of a family of l-adic reps.

http://mathoverflow.net/questions/56571/a-precise-statement-of-the-categorical-version-of-geometric-langlands-conjecture

nLab page on Geometric Langlands