Variation of fundamental groups of curves in positive characteristics

TL;DR

This paper demonstrates that in positive characteristic, the geometric fundamental group varies across fibers in a non-isotrivial family of hyperbolic curves, showing non-constancy of fundamental groups in such families.

Contribution

It establishes the non-constancy of the geometric fundamental group in non-isotrivial hyperbolic curve families over positive characteristic fields.

Findings

Fundamental groups vary in non-isotrivial families

Variation occurs in positive characteristic settings

Fundamental group is not constant across fibers

Abstract

In this paper we prove that given a non-isotrivial family of hyperbolic curves in positive characteristic, the isomorphism type of the geometric fundamental group is not constant on the fibres of the family.