Perverse coherent t-structures through torsion theories

TL;DR

This paper demonstrates that perverse t-structures on derived categories of coherent sheaves can be constructed via tilting torsion theories, extending their applicability to noncommutative projective planes.

Contribution

It shows that perverse t-structures can be obtained through torsion theories, generalizing their construction to quasi-coherent sheaves and noncommutative geometries.

Findings

Perverse t-structures can be derived from tilting torsion theories.

The approach extends to noncommutative projective planes.

Provides a more general framework for perverse t-structures.

Abstract

Bezrukavnikov (later together with Arinkin) recovered the work of Deligne defining perverse $t$-structures for the derived category of coherent sheaves on a projective variety. In this text we prove that these $t$-structures can be obtained through tilting torsion theories as in the work of Happel, Reiten and Smal\o. This approach proves to be slightly more general as it allows us to define, in the quasi-coherent setting, similar perverse $t$-structures for certain noncommutative projective planes.