The Artin-Schreier DGA and the F_p fundamental group of an F_p scheme

TL;DR

This paper demonstrates that the F_p completion of the fundamental group of an F_p scheme can be computed using the bar complex of the Artin-Schreier differential graded algebra, linking algebraic topology and algebraic geometry.

Contribution

It introduces a method to compute the F_p fundamental group via the bar complex of the Artin-Schreier DGA, based on Kats' theorem.

Findings

F_p completion of fundamental group computed by bar complex

Artin-Schreier DGA constructed from relation diagram

Provides a new computational approach for algebraic fundamental groups

Abstract

In this paper, we proved that the F_p completioin of fundamental group of an F_p shceme can be computed by the bar complex of Artien-Schreier differential graded algebra. Artin-Schreier differential graded algebra is obtained by a relation diagram of identity map and frobenius map by Kats' theorem.