Isogenous (non-)hyperelliptic CM Jacobians: constructions, results, and Shimura class groups [1]

Data:

11/05/2022 - 14:30

Aula:

Webinar - Aula virtuale Webex

Speaker:

Bogdan Adrian Dina

Categoria:

Seminari di Algebra e Geometria Algebrica

Afferenza:

Einstein Institute of Mathematics at the Hebrew University in Jerusalem

Descrizione:

Link Webex [2]

Abstract: Jacobians of CM curves are abelian varieties with a particularly large endomorphism algebra, which provides them with a rich arithmetic structure. The motivating question for the results in this talk is whether we can find hyperelliptic and non-hyperelliptic curves with maximal CM by a given order whose Jacobians are isogenous.

Joint work with Sorina Ionica, and Jeroen Sijsling considers this question in genus 3 by using the catalogue of CM fields in the LMFDB, and found a (small) list of such isogenous Jacobians. This talk describes the main constructions, some results, and Shimura class groups.