Computing endomorphism rings and Frobenius matrices of Drinfeld modules

Abstract: Let $\mathbb{F}_q[T]$ be the polynomial ring over a finite field $\mathbb{F}_q$. We study the endomorphism rings of Drinfeld $\mathbb{F}_q[T]$-modules of arbitrary rank over finite fields. We compare the endomorphism rings to their subrings generated by the Frobenius endomorphism and deduce from this a reciprocity law for the division fields of Drinfeld modules. We then use these results to give an efficient algorithm for computing the endomorphism rings and discuss some interesting examples produced by our algorithm. This is a joint work with Sumita Garai.

number theory

Audience: researchers in the topic

Around Frobenius distributions and related topics II