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Reductive embeddings are Cohen-Macaulay

Author: Alvaro Rittatore
Journal: Proc. Amer. Math. Soc. 131 (2003), 675-684
MSC (2000): Primary 14M17, 14M05
Published electronically: October 23, 2002
MathSciNet review: 1937404
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Abstract: In this paper we prove that in positive characteristics normal embeddings of connected reductive groups are Frobenius split. As a consequence, they have rational singularities and are thus Cohen–Macaulay varieties. As an application, we study the particular case of reductive monoids, which are affine embeddings of their unit group. In particular, we show that the algebra of regular functions of a normal irreducible reductive monoid $M$ has a good filtration for the action of the unit group of $M$ .

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Alvaro Rittatore
Affiliation: Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay

Keywords: Reductive embeddings, reductive monoids, Cohen-Macaulay varieties, spherical varieties
Received by editor(s): September 28, 2000
Published electronically: October 23, 2002
Additional Notes: This research was partially done during a stay at the Institut Fourier, Grenoble, France.
Communicated by: Dan M. Barbasch
Article copyright: © Copyright 2002 American Mathematical Society