Operations on t-structures and perverse coherent sheaves

TL;DR

This paper introduces the concepts of consistent pairs and chains of t-structures, proves their lattice structure, and applies this to derive a family of t-structures with hearts called perverse coherent sheaves.

Contribution

It develops a new theoretical framework for understanding t-structures and constructs a family of perverse coherent sheaves using these concepts.

Findings

Proves that two consistent chains generate a distributive lattice.

Constructs a family of t-structures with perverse coherent sheaves as hearts.

Provides a new perspective on the structure of derived categories of coherent sheaves.

Abstract

The notions of consistent pairs and consistent chains of t-structures are introduced. A theorem that two consistent chains of t-structures generate a distributive lattice is proven. The technique developed is then applied to the pairs of chains obtained from the standard t-structure on the derived category of coherent sheaves and the dual t-structure by means of the shift functor. This yields a family of t-structures whose hearts are known as perverse coherent sheaves.