Bruhat-Tits group schemes over higher dimensional base-II
Vikraman Balaji, Yashonidhi Pandey
TL;DR
This paper proves that split reductive Bruhat-Tits group schemes over higher dimensional bases are affine and introduces a new construction method for higher BT-group schemes beyond parahoric types.
Contribution
It extends Yu's construction to higher dimensions and develops a new approach for constructing more general BT-group schemes.
Findings
Split reductive BT group schemes are affine over higher dimensional bases.
A new construction method for higher BT-group schemes is introduced.
The approach generalizes previous constructions beyond parahoric schemes.
Abstract
We prove that split reductive BT group schemes over a higher dimensional base are {\em affine}. Our method also gives a new construction of higher BT-group schemes more general than parahoric ones. The new ingredients are an extension of J.-K.Yu's construction in \cite{yu} to higher dimensional bases, N\'eron-Raynaud dilatations of subgroup schemes on divisors, combined with techniques from \cite{bt2} and the structure theory developed in \cite{bp}.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models