PhD Seminar • Symbolic and Algebraic Computation • Computing Frobenius Actions of Drinfeld Modules Using De Rham and Crystalline Cohomology

Please note: This PhD seminar will take place online.

Joseph Musleh, PhD candidate
David R. Cheriton School of Computer Science

Supervisor: Professor Éric Schost

The close analogy between elliptic curves and Drinfeld modules has motivated substantial interest in translating existing results from the former to the latter. Point counting on elliptic curves is one such problem, with Schoof’s and Kedlaya’s algorithm being among the most well-known algorithms. Both approaches are a consequence of Hasse’s theorem, which bounds the order |E| of an elliptic curve E over a finite field of size q, and relates |E| to the characteristic polynomial of the Frobenius endomorphism on E.

In this work, we will focus on adapting ideas from Kedlaya’s algorithm. To that end, we will discuss the definitions and basic structure of the de Rham and Crystalline cohomology spaces attached to a Drinfeld module, and show how they can be used to speed up the determination of the characteristic polynomial of the Frobenius endomorphism of a Drinfeld module.

To join this PhD seminar on Zoom, please go to https://uwaterloo.zoom.us/j/97393873541.