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


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.


Group Scheme Galois Extension Unipotent Radical Linear Algebraic Group Residue Field 
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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsTufts UniversityMedfordUSA

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