Speaker: Amnon Yekutieli (Ben Gurion Univ.)

Title: Local and Geometric Beilinson-Tate Operators

Abstract: In 1968, Tate introduced a new approach to residues on algebraic curves, based on a certain ring of operators that acts on the completion at a point of the function field of the curve. This approach was generalized to higher dimensional algebraic varieties by Beilinson in 1980. We refer to these operators as global BT operator. Beilinson’s paper had very few details, and his operator-theoretic construction remained cryptic for many years.

In my paper "Local Beilinson-Tate Operators" from about a year ago, I introduced a new ring of operators in the high dimensional setup, with the hope of ellucidating the work of Beilinson. I posed a few conjectures.

In this talk I will explain what are higher topological local fields, how they are obtained from algebraic geometry (Beilinson's higher completion), and the higher residue functional. Next I will discuss the various rings of BT operators (geometric and local). Finally I will state two conjecture regarding BT operators and residue functionals.

Lecture notes are available here.

(updated 23 Dec 2015)