Levi Factors of the Special Fiber of a Parahoric Group Scheme and Tame Ramification

Autor: George J. McNinch
Rok vydání: 2013
Předmět:
Zdroj: Algebras and Representation Theory. 17:469-479
ISSN: 1572-9079
1386-923X
DOI: 10.1007/s10468-013-9404-4
Popis: Let $\cal{A}$ be a Henselian discrete valuation ring with fractions K and with perfect residue field k of characteristic p > 0. Let G be a connected and reductive algebraic group over K, and let $\cal{P}$ be a parahoric group scheme over $\cal{A}$ with generic fiber ${\cal{P}}_{/K} = G$ . The special fiber ${\cal{P}}_{/k}$ is a linear algebraic group over k. If G splits over an unramified extension of K, we proved in some previous work that the special fiber ${\cal{P}}_{/k}$ has a Levi factor, and that any two Levi factors of ${\cal{P}}_{/k}$ are geometrically conjugate. In the present paper, we extend a portion of this result. Following a suggestion of Gopal Prasad, we prove that if G splits over a tamely ramified extension of K, then the geometric special fiber ${\cal{P}}_{/k_{\rm{alg}}}$ has a Levi factor, where k alg is an algebraic closure of k.
Databáze: OpenAIRE
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