Title: Function field Analogue of Shimura’s Conjecture on Period Symbols
Abstract: In this talk, we shall first review the classical story on Shimura’s period symbols and his conjecture, then discuss about our parallel developments on CM periods in the function field setting. In concrete terms, we shall introduce the notion of Shimura’s period symbol over function fields via the periods of “CM dual t-motives”, and establish their fundamental properties. We further formulate and prove a function field analogue of Shimura’s conjecture on the algebraic independence of period symbols. Our results enable us to verify the algebraic independence of the coordinates of any nonzero period vector of a CM abelian t-module with “non-degenerate CM type”. Further applications on special Gamma values will be discussed if time permits. This is joint work with W. Dale Brownawell, Chieh-Yu Chang, and Matthew A. Papanikolas.
Date: Friday, April 1, 2022
Venue: M210, Department of Mathematics, NTNU