The prime-to-p part of \'etale fundamental groups of curves

TL;DR

This paper discusses the prime-to-p part of étale fundamental groups of curves, addressing previous proof issues and presenting a new proof in collaboration with Jeff Yelton, refining understanding of these algebraic structures.

Contribution

Provides a corrected and improved proof of properties of the prime-to-p part of étale fundamental groups of curves, building on and refining prior results.

Findings

New proof of properties of prime-to-p étale fundamental groups

Clarification of previous proof errors

Enhanced understanding of algebraic fundamental groups

Abstract

The previous version of this paper relied on a paper by another author whose proof appears to be invalid in a fundamental way. In arXiv:1707.00649 the author, together with Jeff Yelton, came up with a new proof of almost identical results. (See Remark 1.4 of arXiv:1707.00649.)