Notes on Geometric Langlands
This page will contain a collection of .pdf files intended to share with the community my current understanding of
(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.
- 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)
- Contractibility of the space of rational maps (an "official paper", last updated Jan 17, 2012)
- The Atiyah-Bott formula for the cohomology of Bun(G) (an "official paper", last updated Jan 4, 2015)
- The extended Whittaker category (last updated Dec. 2, 2010)
- Categories over the Ran space (last updated Dec. 2, 2010)
- 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 (an "official" paper, last updated Aug. 26, 2013)
- Stacks (last updated Aug. 14, 2011)
- Quasi-coherent sheaves on stacks (last updated Aug. 18, 2011)
- Sheaves of categories and the notion of 1-affineness (an ``official" paper, last updated Aug. 9, 2014)
- Ind-coherent sheaves (an "official" paper, last updated Oct. 14 , 2012)
- DG Indschemes (an "official" paper, joint with N. Rozenblyum, last updated June 23, 2013)
- Crystals and D-modules (an "official" paper, joint with N. Rozenblyum, last updated Oct. 1, 2014)
- On some finiteness questions for algebraic stacks
(an "official" paper, joint with V. Drinfeld, last updated Oct. 26, 2012)
Chapters from the book project "A study in derived algebraic geometry" by D. Gaitsgory and N. Rozenblyum (prelim version)