Faltings' annihilator theorem and t-structures of derived categories

TL;DR

This paper proves Faltings' annihilator theorem for complexes over CM-excellent rings and classifies t-structures of their bounded derived categories, advancing understanding in algebraic geometry and homological algebra.

Contribution

It establishes the annihilator theorem in a new setting and provides a complete classification of t-structures for certain derived categories.

Findings

Proved Faltings' annihilator theorem for complexes over CM-excellent rings.

Classified all t-structures of the bounded derived category of finitely generated modules.

Enhanced understanding of the structure of derived categories in algebraic geometry.

Abstract

In this paper, we prove Faltings' annihilator theorem for complexes over a CM-excellent ring. As an application, we give a complete classification of the t-structures of the bounded derived category of finitely generated modules over a CM-excellent ring of finite Krull dimension.