Witt ring localized

TL;DR

This paper interprets Witt rings as spaces of vanishing cycles for perverse sheaves, enabling localization of a key isomorphism in Drinfeld's prismatization theory as an integral of an exact triangle.

Contribution

It introduces a novel perspective on Witt rings by relating them to vanishing cycles, allowing localization of a fundamental isomorphism in prismatization theory.

Findings

Witt rings are interpreted as vanishing cycles for perverse sheaves.

A localization of Drinfeld's isomorphism is achieved as an integral of an exact triangle.

Provides a new geometric framework for understanding Witt rings and prismatization.

Abstract

The rings of $p$-typical Witt vectors are interpreted as spaces of vanishing cycles for some perverse sheaves over a disc. This allows to "localize"\ an isomorphism emerging in Drinfeld's theory of prismatization [Dr], Prop. 3.5.1, namely to express it as "an integral"\ of a standard exact triangle on the disc.