An enhanced six-functor formalism for diamonds and v-stacks

TL;DR

This paper extends Scholze's six functor formalism to a broader class of v-stack morphisms using advanced $ abla$-categorical techniques, enhancing the theoretical framework for diamonds and v-stacks.

Contribution

It introduces a generalized six functor formalism for diamonds and v-stacks applicable to a wider range of stacky morphisms, utilizing $ abla$-categorical methods.

Findings

Extended the six functor formalism to more general v-stack morphisms

Developed new $ abla$-categorical techniques for this extension

Provided a unified framework for diamonds and v-stacks

Abstract

This article extends Scholze's six functor formalism for diamonds to a very general class of stacky morphisms between v-stacks, using $\infty$-categorical techniques developed by Liu-Zheng.