On the homotopy exact sequence for log algebraic fundamental groups

TL;DR

This paper develops a log algebraic framework for the homotopy exact sequence of fundamental groups in log geometry, establishing its properties through purely algebraic methods.

Contribution

It introduces a log algebraic version of the homotopy sequence for log varieties and proves its exactness properties algebraically.

Findings

Constructed a log algebraic homotopy sequence for quasi-projective normal crossing log varieties.

Proved exactness properties of the sequence using algebraic methods.

Established foundational results for log algebraic fundamental groups.

Abstract

We construct a log algebraic version of the homotopy sequence for a quasi-projective normal crossing log variety over a log point of characteristic zero and prove some exactness properties of it. Our proofs are purely algebraic.