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summer 2018
 
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Wojciech J. Gajda

professor of mathematics

Mailing address:
Faculty of Mathematics and Computer Science
Adam Mickiewicz University
Umultowska 87, 61-614 Poznań, POLAND
Office: Collegium Mathematicum, B1-35
Phone: +48 (61) 829 5503
Fax: +48 (61) 829 5315
Email: gajda AT amu DOT edu DOT pl

Research interests:

arithmetic geometry, number theory, algebraic topology, algebraic K-theory

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Davide Lombardo, Università di Pisa

10.05.2023 12:00, B1-37

Title: Families of Jacobians with quaternionic multiplication

Abstract:

In joint work with Victoria Cantoral Farfán and John Voight we investigate families of even-dimensional Jacobians defined over Q and admitting an action of the quaternion group. Such abelian varieties are unusual in several ways: for example, their ring of algebraic cycles is not generated by divisor classes, a fact which has consequences both on their arithmetic and on their geometry. We prove that - for every even dimension greater than two - 100% of the members of the families we consider satisfy the Hodge, Tate and Mumford-Tate conjectures, compute their endomorphism rings, and provide explicit generators for their Hodge rings. As a consequence, we show that for such abelian varieties A the minimal field of definition of the endomorphisms and the minimal field over which the Galois representations attached to A have connected image are different.

Last modified: 16.11.2022