Changningphaabi Namoijam, Colby College
Authors: Yen-Tsung Chen and Changningphaabi Namoijam
2023 AWM Research Symposium
Rethinking Number Theory [Organized by Deewang Bhamidipati, Eva Goedhart, and Amita Malik]

Drinfeld introduced what are now called Drinfeld modules, which can be regarded as a function field analogue of elliptic curves. By Anderson’s work, there are higher dimensional generalizations of Drinfeld module called $t$-modules. As they are modules, if we consider two Drinfeld modules $E$ and $F$, we can study the properties of $Ext^1(E,F)$. For example, Papanikolas and Ramachandran showed that elements of $Ext^1(E,F)$ are $t$-modules, and in the case that $F$ is of rank 1 (called the Carlitz module) and $E$ has rank greater than $1$, $Ext^1(E,F)$ itself has the structure of a $t$-module. In this talk, we present recent work regarding the elements of $Ext^1(E,F)$ when $E$ and $F$ have arbitrary rank. This is joint work with Yen-Tsung Chen.

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