Number Theory Seminar: Symplectic Reidemeister torsion and symplectic L-functions

SEMINARS, NUMBER THEORY

Speaker:

Akshay Venkatesh - IAS

Many of the quantities appearing in the conjecture of Birch and Swinnerton-Dyer look suspiciously like squares. Motivated by this and related examples, we may ask if the central value of an L-function "of symplectic type" admits a preferred square root.

The answer is no: there's an interesting cohomological obstruction. More formally, in the everywhere unramified situation over a function field, I will describe an explicit cohomological formula for the L-function modulo squares. This is based on a purely topological result about 3-manifolds. If time permits I'll speculate on generalizations. This is based on joint work with Amina Abdurrahman.

https://people.math.harvard.edu/~sli/hnts/