Derived Logarithmic Geometry I

TL;DR

This paper develops foundational aspects of logarithmic derived geometry by introducing a model category of logarithmic simplicial rings, defining derived log étale maps, and establishing derived log stacks.

Contribution

It introduces a new model category framework for logarithmic simplicial rings and defines derived log étale maps and stacks, advancing the theoretical foundation of logarithmic derived geometry.

Findings

Established a model category of logarithmic simplicial rings.

Defined derived log étale maps within this framework.

Introduced the concept of derived log stacks.

Abstract

In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \'etale maps and use this to define derived log stacks.