Vladimir Drinfeld

Infinite-Dimensional Vector Bundles in Algebraic Geometry

The goal of this work is to show that there is a reasonable algebro-geometric notion of vector bundle with infinite-dimensional locally linearly compact fibers and that these objects appear “in nature.” Our approach is based on some results and ideas discovered in algebra during the period 1958–1972 by H. Bass, L. Gruson, I. Kaplansky, M. Karoubi, and M. Raynaud.

Geometric constant term functor(s)

We study the Eisenstein series and constant term functors in the framework of geometric theory of automorphic functions. Our main result says that for a parabolic

On a strange invariant bilinear form on the space of automorphic forms

P\subset G

On braided fusion categories I

P⊂G with Levi quotient M, the !-constant term functor

Infinite-dimensional vector bundles in algebraic geometry (an introduction)

\begin{aligned}{\text {CT}}_!:{\text {D-mod}}({\text {Bun}}_G)\rightarrow {\text {D-mod}}({\text {Bun}}_M)\end{aligned}

A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic

CT!:D-mod(BunG)→D-mod(BunM)is canonically isomorphic to the *-constant term functor