45 citations · 309 across the 42 of their papers we have counts for
30 papers · 1 filter
Abelian varieties are not quotients of low-dimension Jacobians
Jacob Tsimerman
We prove that for any two integers and , there exist abelian varieties over which are not quotients of a Jacobian of dimension .…
Finite Orbits in Surfaces with a Double Elliptic Fibration and Torsion Values of Sections
Pietro Corvaja, Jacob Tsimerman, Umberto Zannier
We consider surfaces with a double elliptic fibration, with two sections. We study the orbits under the induced translation automorphisms proving that, under natural conditions, th…
Non-trivial bounds on 2, 3, 4, and 5-torsion in class groups of number fields, conditional on standard -function conjectures
Arul Shankar, Jacob Tsimerman
We prove new conditional bounds on the the -torsion of class groups of number fields of any fixed degree, for , , , and . Our methods first recast the problem in t…
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.
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…
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…