A twist on ring morphisms and crepant contractions

TL;DR

This paper develops a new framework for constructing and understanding spherical twists in derived categories, especially around ring morphisms and crepant contractions, extending previous work in noncommutative geometry.

Contribution

It introduces a construction of twist functors around ring morphisms and proves their autoequivalence, connecting noncommutative twists to spherical twists in a new way.

Findings

Noncommutative twist by Donovan and Wemyss is a spherical twist.

Constructs new spherical twists for singular schemes.

Extends previous results on twists induced by crepant contractions.

Abstract

Given a ring morphism, this paper constructs the twist functor around the induced derived restriction of scalars functor. We prove that the twist around ring morphisms is a derived autoequivalence in the setting of twists induced by Frobenius exact categories. As a corollary, it is shown that the noncommutative twist introduced by Donovan and Wemyss is in fact a spherical twist around the restriction of scalars functor. We then use this technology to obtain new spherical twists for singular schemes, and discuss how our result extends previous works on spherical twists induced by crepant contractions.