Symplectic Reidemeister torsion and symplectic L-functions
SEMINARS: NUMBER THEORY
When: September 14, 2022
3:00 pm - 4:00 pm
Where: Science Center 507
Address:
1 Oxford Street, Cambridge, MA 02138, United States
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.