Mutations and derived equivalences for commutative noetherian rings

TL;DR

This paper explores how the prime spectrum of a commutative noetherian ring influences mutations of cosilting objects in its derived category, providing new insights into the structure of these algebraic objects.

Contribution

It introduces a novel approach to describe mutations of cosilting objects using the prime spectrum of commutative noetherian rings.

Findings

Prime spectrum controls mutation behavior.

Description of cosilting mutations via prime spectrum.

New connections between spectrum and derived category structures.

Abstract

The representation theory of a commutative noetherian ring is tightly controlled by its prime spectrum. In this article we use the prime spectrum to describe mutation of cosilting objects in the derived category of a commutative noetherian ring.