Compatibility of t-structures in a semiorthogonal decomposition

TL;DR

This paper presents a method to construct a global t-structure from a semiorthogonal decomposition with compatible t-structures on components, generalizing Bondal's theorem on exceptional sequences.

Contribution

It introduces a way to derive a global t-structure from component t-structures in a semiorthogonal decomposition, extending existing theorems.

Findings

Global t-structure construction from semiorthogonal decomposition

Generalization of Bondal's theorem on exceptional sequences

Compatibility conditions for component t-structures

Abstract

We describe how to obtain a global t-structure from a semiorthogonal decomposition with compatible t-structures on every component. This result is used to generalize a well-known theorem of Bondal on full strong exceptional sequences.