Descent for semiorthogonal decompositions

TL;DR

This paper develops descent theorems for semiorthogonal decompositions in derived categories, employing derived algebraic geometry techniques to handle more general filtrations and marked filtrations.

Contribution

It introduces new descent theorems that extend semiorthogonal decompositions to broader contexts, including marked filtrations and preferred objects.

Findings

Established descent theorems for semiorthogonal decompositions.

Enabled descent of more general filtrations and marked filtrations.

Provided a framework for descending not only subcategories but also specific objects.

Abstract

We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not only admissible subcategories but also preferred objects.