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Fundamental Lemma Seminar
Here are some topics and materials related to Ngo's Fundamental Theorem of Endoscopy.
Background Reading
- Arthur's Stability and Endoscopy: Informal Motivation
- Langland's Shaw Prize Reflections
- Dat's Bourbaki Report (French)
The Proof
- Ngo's Proof (French)
- Ngo's geometric interpretation (French)
- Ngo's ICM talk (French)
- Chicago's seminar on the Fundamental Lemma, including Drinfeld's notes.
- Witten-Frenkel's Mirror Symmetry approach to Geometric Endoscopy
- Hitchin's Langlands duality and G2 spectral curves
- Laumon's slides
Earlier Partial Results and Methods
- Unitary Groups (Laumon, Ngo)
- Laumon slides
Proof Machinery
Stable Trace Formua
- Harris's book Stable trace formula and applications
- Harris's essay Introduction to the stable trace formula
- Labesse's stablization of the twisted trace formula
Affine Springer Fibers
- Bezrukavnikov “Dimension of the Fixed Point Sets on Affine Flag Manifolds” Math. Research Letters, 4 (1996), 185-189.
Hitchin fibration and Higgs Bundles
- Bradlow et al. What is a Higgs bundle?
- Nadler's Springer theory via the Hitchin fibration
- Gaitsgory and Donagi: The gerbe of Higgs bundles
- Gothen's thesis
Perverse Sheaves and the BBD decomposition theorem
- de Cataldo and Migliorini’s Introduction to perverse sheaves and the decomposition theorem
- Rietsch's An introduction to perverse sheaves
- Kleiman's Introduction to intersection homology theory expanded version
- Dimca's book Sheaves in Topology (google book)
- Kirwin and Woolf's An introduction to intersection homology theory (google book)
- Gelfand and Manin's Homological Algebra (google book)
- Ryoshi Hotta, Kiyoshi Takeuchi and Toshiyuki Tanisaki: D-Modules, Perverse Sheaves, and Representation Theory (table of contents only)
Stacks
- stack project