Seminarios Ta de Números

A Galois Equivariant Class Number Formula for Drinfeld L-functions

SPEAKER: Nathan Green (UCSD)

DATE & TIME: Tuesday, April 06th, 2021 - 17:30

ABSTRACT: Classically, the class number formula relates the residue of the Dedekind zeta function at 1 with the class number and the regulator of a given number field. Recently, Taelman gave an analogue of the class number formula for function fields using the L-function attached to a Drinfeld module. In this setting, however, the class number is replaced by a generator of the Fitting ideal of the "class module" coming from Galois cohomology and the regulator is replaced by the index of two naturally occurring lattices coming from the Drinfeld module structure. In our work, we generalize Taelman’s class number formula to the Galois equivariant setting and give a volume interpretation of the L-value which can be viewed as an equivariant
Tamagawa number formula for Drinfeld L-values. Joint work with Joseph Ferrara, Zach Higgins and Cristian Popescu.