Geometric Langlands Seminar

Some texts related to the talks at the seminar

• Forget-me-nots and Footboards. You might have heard these words mentioned on the seminar. If you ever wondered what they meant, here's an explanation.
• Illusie on Grothendieck's Seminar in IHES (Audio in WAV).

Langlands conjecture

• Langlands' works.
• Automorphic Forms, Representaions, and L-Functions (Proceedings of a conference in Corvallis), A.Borel and W.Casselman (editors), AMS, 1979). Very useful for those intereseted in the Langlands program. PDF available from the AMS site: Volume 1, Volume 2.
• Algebraic Groups and Discontinuous Subgroups, A.Borel and G.Mostow (editors), AMS, 1966. PDF available from the AMS site.

Fundamental Lemma and Endoscopy (new version!)

• Le Lemme Fondamental pour les Algebres de Lie, Bao Chau Ngo, e-print available here
• Drinfeld's notes on the local Tate-Nakayama duality and its interpretation due to Kottwitz: PDF
• The article by Kottwitz mentioned in these notes: PDF
• Drinfeld's notes on Kostant's theorem: PDF
• The e-print by Beilinson and Drinfeld mentioned in these notes is available here
• Drinfeld's notes on centralizers of semisimple elements of semisimple groups: PDF
• Drinfeld's notes in which he reformulates (a part of) the Fundamental Lemma for SL(n) in very concrete and "classical" terms: PDF
• An example of an endoscopy group that is not a subgroup of the ambient group: PDF
• Drinfeld's notes for his lecture on regular centralizers: PDF
• Drinfeld's notes for his lecture on the Hitchin fibration: PDF

Some useful books available online

• SGA (but the quality is not very good).
• Current Trends in Arithmetical Algebraic Geometry, K. Ribet (editor), AMS, 1987. PDF available from the AMS site.
• Invitation to higher local fields, I.Fesenko and M.Kurihara (editors). Available as PS or PDF from the G&T site.

Derived category of quasicoherent sheaves

• Synopsis of Bezrukavnikov's talks on the Thomason-Trobaugh Theorem (DVI, PostScript).

Algebraic K-theory

• Notes on Quillen's constructions of K-groups (DVI, PostScript).
• Beilinson's comments on Bloch's lecture of 11.3.03 (DVI, PostScript).

Cobordism theory

• J.Morava's notes on cobordism theory. (DVI, PostScript). Updated on 08/02.

Motives

• V.Voevodsky, Lectures in Motivic Cohomology. Notes by C.Mazza and C.Weibel, available on Weibel's page.

Noncommutative geometry

• M.Kontsevich's course at ENS, 1998 (French). Course notes in PostScript.
  A related letter from M.Kontsevich to A.Beilinson. Text.
• B.Tsygan, Cyclic Homology. (Preliminary version). PostScript, DVI.
• V.Drinfeld, DG quotients of DG categories. E-preprint.
• B.Keller, Introduction to A-infinity algebras and modules. E-preprint.
• K.Lefevre-Hasegawa, Sur les A-infini categories. Thesis available from author's page.
• M.Kontsevich's course on deformation theory. Course notes in PostScript.
• V.Ginzburg, Lectures on noncommutative geometry. E-preprint.
• A.Bondal, M.Van den Bergh, Generators and representability of functors in commutative and noncommutative geometry. E-preprint.
• The derived category of finite-dimensional representations of a quiver is an important and somewhat unusual example of a smooth proper DG category. See Crawley-Boevey's home page ,  the Miyachi-Yekutieli e-print math.RA/9904006 , the Appendix of Yekutieli's e-print math.RA/9810134, and pages 13, 16-18, 21, 23, 24 of Kontsevich's ENS course.
• Notes of Arinkin's talk on deformation qunatization and the Fourier-Mukai transform (04/06/06). (DVI, PostScript).

Some lecture notes and articles by Joseph Bernstein

• Course on D-modules (PostScript, DVI).
• Course on representations of p-adic groups (PostScript, DVI).
• Second adjointness for representations of reductive p-adic groups (PostScript, DVI).
• Meromorphic continuation of Eisenstein series: Lecture I (PostScript, DVI), Lecture II (PostScript, DVI), Lecture III (PostScript, DVI), Lecture IV (PostScript, DVI), Lecture V (PostScript, DVI).

The determinant of cohomology and microlocalization (after A. Beilinson)

• A. Beilinson, Topological $\epsilon$-factors. E-preprint.
• `Appendix: The case of a surface' by A. Beilinson (PDF).

Epsilon-factors for the period determinants on curves

Some texts by Beilinson and Drinfeld

• Chiral algebras (preliminary version, PDF). Contents, Introduction, Chapter 1, Chapter 2, Chapter 3, Chapter 4, References, Index.
• Quantization of Hitchin's integrable system and Hecke eigensheaves (preliminary version, PostScript). Pages 1-100, Pages 101-200, Pages 201-300, Pages 301-384.
• The same text in PDF (one file).

Geometric Langlands conjecture and beyond

• V.Drinfeld, Infinite-dimensional vector bundles in algebraic geometry, notes of the talk at the `Unity of Mathematics' conference (E-preprint). Expanded version: (PostScript, PDF).