Filtrations and Buildings
Christophe Cornut (IMJ)
TL;DR
This paper develops a scheme-theoretic framework for Tits vectorial buildings, connecting filtrations on fiber functors to Bruhat-Tits buildings with a Tannakian perspective.
Contribution
It introduces a scheme-theoretic approach to Tits buildings and links filtrations on fiber functors to Bruhat-Tits structures, offering a Tannakian interpretation.
Findings
Constructed a scheme-theoretic version of Tits vectorial buildings.
Related filtrations on fiber functors to Bruhat-Tits buildings.
Provided a Tannakian description of these structures.
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 Bruhat-Tits buildings, for which we also provide a Tannakian description.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory