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Artin comparison theorem, etale fundamental group, l-adic
cohomology
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La dualité de Poincaré et la cohomologie à support compact
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Lefschetz hyperplane theorem, characteristic class, Steenrod
square
-
automorphy lifting: lecture 17-19
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Spectra motivation
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Hamiltonian, Noether’s theorem, spherical varieties
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Proper base change
-
Katz’s new proof of RH for curves and hypersurfaces over finite
fields
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Deligne-Lusztig theory
-
automorphy lifting: Lecture 14-16
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Spectral sequence
-
Newton polygon and non-archimedean holomorphic functions
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Operads
-
Monoidal categories and monoidal functors
-
automorphy lifting: Lecture 10-13
-
Zariski-etale comparison, cohomology of curves
-
Dessin d’enfant
-
faisceaux constructibles
-
Etale sites are topological invariants
-
Slick way of proving Kunneth formula
-
Gelfand trick
-
Des théories de cohomologie de Weil
-
Homotopy theory intro and Model category
-
automorphy lifting lecture 7-9
-
La fonction zêta d’un schéma sur un corps fini
-
Deligne-Lusztig theory algebraic group preliminaries
-
Local acyclicity and smooth base change
-
Adic spaces: Chapter 2 and 3 of Scholze-Weinstein’s Berkley Lecture’s
on
-adic geometry
-
Lurie’s higher topos takeaway
-
Pro-unipotent completion
-
revenir sur GAGA
-
Why should we believe Mordell’s conjecture aka Faltings’s theorem
-
Automorphic lifting lecture 4-6
-
Abelian Galois representation implies potentially good reduction
-
Quadratic twist of elliptic curve
-
Le théorème de Serre sur les variétés kählériennes (analogue des
conjectures de Weil dans le cas complexe)
-
Automorphic lifting: Lecture 1-3
-
Obstruction theory
-
What comes before Deligne Lusztig theory
-
Le théorème de l’indice de Hodge : le cas du corps des nombres
complexes
-
La conjecture de Weil
-
p-divisible groups and what they are for
-
Exercises on Algebraic Geometry
-
Qualifying exam questions: Complex Analysis
-
Qualifying exam question (Real Analysis, Measure Theory, Functional
Analysis)
-
Qualifying exam question (Algebraic topology)
-
Qualifying exam question (Algebra, Representation theory, Category
Theory and Homological Algebra)
-
Hilbert’s tenth problem: How additive combinatorics comes into
play
-
Hilber’s Tenth Problem: Recent Development
-
Proof of Mordell-Lang for function fields in characteristic zero
using differential algebra