p-torsion étale sheaves on the Jacobian of a curve (2019). arXiv:1909.12462.
A simple categorification of the geometric Artin reciprocity with p-torsion coefficients.
Extensions by K2 and factorization line bundles (2019, with James Tao). arXiv:1901.08760.
Factorization line bundles on the Beilinson-Drinfeld affine Grassmannian are classified by certain K-theoretic data.
Quantum parameters of the geometric Langlands theory (2017). arXiv:1708.05108.
The theory of quasi-twistings as a way to formalize the degeneration κ→∞ in the global geometric Langlands program; local versions of the construction are available in §4 of my Paris notes.
Maximally Frobenius-destabilized vector bundles over smooth algebraic curves. arXiv:1408.5117. International Journal of Mathematics 28.02 (2017): 1750003.
When a vector bundle becomes maximally unstable after Frobenius pullback, we can learn a lot about the stability of the bundle itself, and the result is different depending on whether its rank is larger than, equal to, or lower than the characteristic p.
Limiting behavior of Donaldson's heat flow on non-Kähler surfaces (2014, with Jacob McNamara). arXiv:1403.8037.
Lifting representations of finite reductive groups: a character relation (with Jeffrey Adler et al). arXiv:1205.6448. Involve, a Journal of Mathematics 9.5 (2016): 805-812.
Teaching: étale cohomology (Fall 2019)
Here is the course homepage.
Seminar: ind-coherent sheaves (Spring 2016)
Seminar on derived algebraic geometry, with an emphasis on the theory of ind-coherent sheaves. Here is the seminar homepage.
(Warning: I make mistakes! If you find them, email me.)
Pro-excision of algebraic K-theory. pdf.
Notes on the pro-excision theorem for abstract blow-up squares due to Kerz-Strunk-Tamme.
Cayley-Hamilton theorem and Eichler-Shimura relations. pdf.
Notes on Vincent Lafforgue's Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale, section 7.
What is the Hecke eigenproblem? pdf.
Notes on the problem of finding Hecke eigen-D-modules.
The Bondal-Orlov reconstruction theorem. pdf.
How to recover a smooth projective variety with ample (or anti-ample) canonical bundle from its derived category of coherent sheaves.
Deligne's theorems on degeneration of spectral sequences. pdf.
Leray spectral sequence and Hodge-de Rham spectral sequence.
Finite and abelian affine group schemes. pdf.
Cartier duality, étale group schemes, group schemes of multiplicative type.
Tensor product of semistable vector bundles over curves in characteristic zero. pdf.
Namely, the tensor product is still semistable. Almost all technical ingredients are explained in detail.
Other things that you may find funny
My face. Link.