Towards the motivic Nagao's conjecture and its connections with the Tate conjectures

Abstract: In 1997, Nagao conjectured that the rank of an elliptic surface could be given by a limit formula arising from a weighted average of Frobenius traces from each fiber. During this talk, I would like to report on a joint work with S. Kim where we introduced, for the first time, the Motivic Nagao conjecture for pure motives. In addition, I will highlight as well its links with some well-known conjectures in arithmetic geometry.

number theory

Audience: researchers in the topic

Around Frobenius distributions and related topics II