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Algebras and Representation Theory

, Volume 17, Issue 2, pp 469–479 | Cite as

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

  • George J. McNinchEmail author
Article

Abstract

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.

Keywords

Group Scheme Galois Extension Unipotent Radical Linear Algebraic Group Residue Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA

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