
TL;DR
This paper extends the understanding of how certain group schemes over local fields are determined by their truncated data, focusing on parahoric group schemes in the context of Bruhat-Tits theory.
Contribution
It proves an analogous congruence result for parahoric group schemes, generalizing previous results known for tori to the setting of reductive groups.
Findings
Established a canonical determination of parahoric group schemes from truncated data.
Extended Chai and Yu's results from tori to reductive groups.
Provided a new framework for understanding congruences of group schemes.
Abstract
Let be a non-archimedean local field and let be a torus over . With denoting the N\'eron-Raynaud model of , a result of Chai and Yu asserts that the model is canonically determined by for , where with denoting the natural projection of on , and . In this article we prove an analogous result for parahoric group schemes attached to facets in the Bruhat-Tits building of a connected reductive group over .
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