Stability conditions under change of base field

TL;DR

This paper studies how Bridgeland stability conditions on algebraic varieties behave when changing the base field, especially for finite Galois extensions, showing an embedding property of stability manifolds.

Contribution

It proves that the stability manifold of a variety over a field embeds as a closed submanifold into that of its base change under finite Galois extensions.

Findings

Stability manifold embeds as a closed submanifold under Galois extension

Results apply to varieties over arbitrary fields

Provides new insights into stability conditions under base change

Abstract

We investigate the behaviour of Bridgeland stability conditions under change of base field with particular focus on the case of finite Galois extensions. In particular, we prove that for a variety X over a field K and a finite Galois extension L/K the stability manifold of X embeds as a closed submanifold into the stability manifold of the base change variety.