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


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September 14, 2022 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

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.