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math.NT2025

Abelian varieties not isogenous to Jacobians over global fields

Ananth N. Shankar, Jacob Tsimerman

We prove the existence of abelian varieties not isogenous to Jacobians over characterstic function fields. Our methods involve studying the action of degree Hecke operators…

math.NT2024

Canonical Heights on Shimura Varieties and the André-Oort Conjecture

Jonathan Pila, Ananth N. Shankar, Jacob Tsimerman +2

The main purpose of this work is to prove the André-Oort conjecture in full generality.

math.NT2024

Towards an Elementary Formulation of the Riemann Hypothesis in Terms of Permutation Groups

Will Cavendish, Jacob Tsimerman

This paper investigates the relationship between the Riemann hypothesis and the statement , where is the maximum order of an element of…