A computation on Drinfeld modules

Abstract: The development of algebraic geometry has shed light on deep similarities between the classical number theory (characteristic zero, number fields), and its positive characteristic analogue (centered on curves and function fields). The latter turned out easier to work with: from a theoretical point of view, some results are unconditional (e.g. Riemann hypothesis for function fields); from a computational point of view, a lot of elementary procedures can be performed efficiently (e.g. polynomial factorization, as opposed to integer factorization).

In this talk, we will motivate Drinfeld modules: objects that play the role for function fields that elliptic curves play for number fields. We will give the example of the computation of a group action from Class Field Theory whose classical analogue is used in isogeny-based cryptography, and rather slow to compute.

algebraic geometrynumber theory

Audience: researchers in the discipline

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SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca

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