Hochschild homology for log schemes

TL;DR

This paper extends Hochschild and cyclic homology theories to log schemes, algebraic spaces, and stacks, providing a broader framework for their application in algebraic geometry.

Contribution

It introduces a generalization of Hochschild and cyclic homology to log schemes, algebraic spaces, and stacks, expanding their applicability.

Findings

Generalized Hochschild homology to log schemes and stacks

Established new relationships between homology theories and log structures

Provided tools for future research in algebraic geometry involving log schemes

Abstract

We extend the notions of Hochschild and cyclic homology to morphisms from algebraic spaces to algebraic stacks. Using this, we obtain generalizations to log schemes in the sense of Fontaine and Illusie of these homology theories.