Spanning isogeny classes of principally polarized abelian surfaces with RM

TL;DR

This paper develops a method to decompose isogenies between principally polarized abelian surfaces with real multiplication, enabling enumeration of their isogeny classes, which advances understanding in algebraic geometry and number theory.

Contribution

It introduces a novel decomposition strategy for isogenies in abelian surfaces with RM, facilitating enumeration of their isogeny classes.

Findings

Decomposition of isogenies into elementary types

Strategy for enumerating isogeny classes

Enhanced understanding of abelian surfaces with RM

Abstract

We describe how isogenies between principally polarized abelian surfaces (PPAS) with real multiplication (RM) can be decomposed into elementary isogeny types. This leads to a strategy for enumerating the isogeny class of a given PPAS with RM. This note is part of an ongoing work with R. van Bommel, S. Chidambaram, and E. Costa and is not indended for separate publication.