Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups

TL;DR

This paper presents a method to explicitly construct different topological or geometric data that produce isomorphic tempered fundamental groups for certain algebraic varieties over p-adic fields, highlighting new ways to understand their fundamental group structures.

Contribution

The paper introduces a novel explicit construction of isomorphic tempered fundamental groups from distinguishable geometric data, advancing the understanding of fundamental group representations over p-adic fields.

Findings

Explicit constructions of isomorphic fundamental groups from distinguishable data

Demonstrates topological and geometric distinguishability despite group isomorphism

Provides new tools for studying fundamental groups in p-adic geometry

Abstract

I show that one can explicitly construct topologically/geometrically distinguishable data which provide isomorphic copies (i.e. \emph{isomorphs}) of the tempered fundamental group of a geometrically connected, smooth, quasi-projective variety over $p$-adic fields.