The splitting principle and singularities

TL;DR

This paper generalizes the splitting principle in derived categories, providing a unified framework that enhances understanding and characterization of various singularities in algebraic geometry.

Contribution

It proves a broad, unifying statement of the splitting principle that encompasses and improves upon previous specific results related to singularities.

Findings

Unified framework for splitting principle

Improved characterizations of rational and DB singularities

General theorem covering multiple previous results

Abstract

The splitting principle states that morphisms in a derived category do not "split" accidentally. This has been successsfully applied in several characterizations of rational, DB, and other singularities. In this article I prove a general statement that implies many of the previous individual statements and improves some of the characterizations in the process.