Measuring birational derived splinters

TL;DR

This paper explores categorical methods to study birational derived splinters, extending rational singularities beyond characteristic zero fields, and introduces a derived category invariant called 'level' to measure their failure.

Contribution

It introduces the concept of birational derived splinters and demonstrates how the 'level' invariant in the derived category quantifies their singularities.

Findings

The 'level' invariant measures the failure of birational derived splinters.

Extension of rational singularities concept beyond characteristic zero.

Categorical methods provide new insights into singularity study.

Abstract

This work is concerned with categorical methods for studying singularities. Our focus is on birational derived splinters, which is a notion that extends the definition of rational singularities beyond varieties over fields of characteristic zero. Particularly, we show that an invariant called `level' in the associated derived category measures the failure of these singularities.