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Filtrations and Buildings

About this Title

Christophe Cornut

Publication: Memoirs of the American Mathematical Society
Publication Year: 2020; Volume 266, Number 1296
ISBNs: 978-1-4704-4221-7 (print); 978-1-4704-6255-0 (online)
DOI: https://doi.org/10.1090/memo/1296
Published electronically: July 22, 2020
Keywords: Filtrations, buildings and the Tannakian formalism.
MSC: Primary 14L15, 18D10, 20E42, 20G05, 51E24

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Table of Contents

Chapters

  • 1. Introduction
  • 2. The group theoretical formalism
  • 3. The Tannakian formalism
  • 4. The vectorial Tits building $\mathbf {F}^{\Gamma }(G)$
  • 5. Affine $\mathbf {F}(G)$-buildings
  • 6. Bruhat-Tits buildings

Abstract

We construct and study a scheme theoretical version of the Tits vectorial building, relate it to filtrations on fiber functors, and use them to clarify various constructions pertaining to affine Bruhat-Tits buildings, for which we also provide a Tannakian description.

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