Contracting endomorphisms and dualizing complexes

TL;DR

This paper explores how contracting endomorphisms, like the Frobenius map, can be used to identify dualizing complexes over commutative local noetherian rings, linking homological properties to duality theory.

Contribution

It provides new criteria for detecting dualizing complexes via homological properties of contracting endomorphisms, especially in positive characteristic.

Findings

Homological properties of contracting endomorphisms characterize dualizing complexes.

Frobenius endomorphism plays a key role in positive characteristic cases.

New detection methods for dualizing complexes based on endomorphism behavior.

Abstract

We investigate how one can detect the dualizing property for a chain complex over a commutative local noetherian ring R. Our focus is on homological properties of contracting endomorphisms of R, e.g., the Frobenius endomorphism when R contains a field of positive characteristic.