Cristaux et immeubles

TL;DR

This paper explores the structure of crystals within G-isocrystals over Q_p using Bruhat-Tits buildings, revealing a geometric perspective on their organization and minimality properties.

Contribution

It introduces a novel geometric framework for understanding crystals in G-isocrystals via Bruhat-Tits buildings, linking algebraic and metric space concepts.

Findings

Crystals form tubular neighborhoods around a minimal skeleton.

Bruhat-Tits buildings provide a natural setting for analyzing G-isocrystals.

The minimality property characterizes the structure of these neighborhoods.

Abstract

Let G be a connected reductive group defined over Q_p. The set of crystals contained in a given G-isocrystal is viewed from a Bruhat-Tits building-theoretic vantage point as a kind of tubular neighborhood of a skeleton characterized by a minimality property arising from metric space theory.