Notes on Geometric Langlands

This page will contain a collection of .pdf files intended to share with the community my current understanding of Geometric Langlands
(global and local, classical and quantum).

Not all papers that appear in the list of references are ready to be posted, but most of them exist in one form or another, and you're
welcome to request a .pdf file from me. Otherwise, I'll be posting them gradually.

Needless to say, comments and corrections of any kind are extremely welcome!

Note on the status of the assertions:

If a statement is designated as a "Theorem", this means that the proof exists (but may have not been written down yet).

If a statement is designated as a "Quasi-Theorem", this means that I see a way how to prove it, but haven't thought through the details.
If you are a graduate student or a post-doc interested in the area, you are welcome to supply a proof and claim the result.

Papers:

Constructions on Bun(G)

• Compact generation of the category of D-modules on Bun(G) (an "official" paper, joint with V. Drinfeld, last updated Feb. 28, 2013)
• Verdier duality on Bun(G) (last updated Dec. 8, 2010)
• The extended Whittaker category (last updated Dec. 2, 2010)
• Categories over the Ran space (last updated Dec. 2, 2010)
• Contractibility of the space of rational maps (an "official paper", last updated Jan 17, 2012)
• Singular support of coherent sheaves, and the geometric Langlands conjecture (an "official paper", joint with D. Arinkin, last updated Feb. 26, 2013)
• Outline of the proof of the geometric Langlands conjecture for GL(2) (an "official paper", last updated Feb. 11, 2013)

Eisenstein series

• Geometric constant term functor(s) (an "official" paper, joint with V. Drinfeld, last updated Nov. 28, 2010)
• A "strange" functional equation for Eisenstein series (an "official" paper, joint with V. Drinfeld, last updated Nov. 24, 2010)

Foundational stuff

• Generalities on DG categories (last updated Dec. 30, 2012)
• Filtered colimits of categories, by N.~Rozenblyum (last updated Dec. 30, 2012)
• Functors given by kernels, adjunctions and duality (last updated March 11, 2013)
• Stacks (last updated Aug. 14, 2011)
• Quasi-coherent sheaves on stacks (last updated Aug. 18, 2011)
• Sheaves of categories over prestacks (last updated Jan. 5, 2013)
• Ind-coherent sheaves (an "official" paper, last updated Oct. 14 , 2012)
• DG Indschemes (an "official" paper, joint with N. Rozenblyum, last updated Nov. 10, 2012)
• Crystals and D-modules (an "official" paper, joint with N. Rozenblyum, last updated Nov. 8, 2011)
• On some finiteness questions for algebraic stacks (an "official" paper, joint with V. Drinfeld, last updated Oct. 26, 2012)