Frobenius distribution in number theory over function fields

Abstract: There exists a natural analogue of the Chebotarev density theorem for the field of rational functions in one variable over a finite field, or extensions of it. Because of the additional geometric flexibility of that setting, this theorem can be used to prove number-theoretic statements over that field which have little or no apparent relationship to Chebotarev. I will explain an example of this phenomenon in my work with Michael Lipnowski and Jacob Tsimerman on the Cohen-Lenstra heuristics over function fields.

number theory

Audience: researchers in the topic

Around Frobenius distributions and related topics II