# Grauert-Riemenschneider Vanishing via modulus sheaves with transfers

## TL;DR

This paper shows that the Grauert-Riemenschneider Vanishing Theorem can be derived from the theory of modulus sheaves with transfers, and provides a new way to characterize rational singularities in characteristic zero.

## Contribution

It demonstrates that classical vanishing theorems follow from modulus sheaves with transfers and introduces a novel characterization of rational singularities.

## Key findings

- Grauert-Riemenschneider Vanishing follows from modulus sheaves with transfers
- New characterization of rational singularities in characteristic 0
- Connections between classical theorems and modern sheaf theory

## Abstract

We observe that the classical Grauert-Riemenschneider Vanishing Theorem is a direct consequence of basic results from the theory of modulus sheaves with transfers as developed by Kahn-Saito-Yamazaki. We also obtain a new characterization of rational singularities in characteristic 0.

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Source: https://tomesphere.com/paper/1902.10018