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Texas A&M University

Number Theory Seminar

Date: November 21, 2023

Time: 11:10AM - 12:10PM

Location: BLOC 302

Speaker: Yen-Tsung Chen, Penn State University


Title: On periods of extensions of Drinfeld modules by the Carlitz module

Abstract: In 1973, Drinfeld introduced the notion of elliptic modules, now called Drinfeld modules, which can be viewed as a function field analogue of elliptic curves. Anderson introduced higher dimensional generalizations of Drinfeld modules, called t-modules. It was shown by Papanikolas and Ramachandran that there is a special subgroup Ext^1_0(E, C) of extensions of a Drinfeld module E by the Carlitz module C(a special rank 1 Drinfeld module) that has a t-module structure naturally and is isomorphic to the dual t-module associated with E. In this talk, we study the periods of the extensions in Ext^1_0(E, C) and establish their connection with the periods and logarithms of the dual t-module associated with E. Our result generalizes the work of Chang for rank 2 Drinfeld modules. This is joint work with Changningphaabi Namoijam.