Homological characterization of regularity in Logarithmic Algebraic Geometry

TL;DR

This paper provides a homological criterion for log regularity in logarithmic algebraic geometry by linking it to the vanishing of (co)homology of the logarithmic cotangent complex.

Contribution

It introduces a homological characterization of K. Kato's log regularity using the vanishing of (co)homology of the logarithmic cotangent complex.

Findings

Homological criterion for log regularity established

Vanishing of (co)homology characterizes log regularity

Connects log regularity with cotangent complex properties

Abstract

We characterize K. Kato's log regularity in terms of vanishing of (co)homology of the logarithmic cotangent complex.