Cocharacter-closure and spherical buildings

2015/06/01 by Michael Bate, Sebastian Herpel, Bate, Michael +5
Mathematics · #14L24 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14L24 #msc:20G15

paper · pdf · doi:10.48550/arxiv.1506.00539

16 pages; v 2 17 pages, exposition improved; to appear in the Robert Steinberg Memorial Issue of the Pacific Journal of Mathematics

arxiv created 2015/09/28 · arxiv updated 2015/09/29

Abstract

Let k be a field, let G be a reductive k-group and V an affine k-variety on which G acts. In this note we continue our study of the notion of cocharacter-closed G(k)-orbits in V. In earlier work we used a rationality condition on the point stabilizer of a G-orbit to prove Galois ascent/descent and Levi ascent/descent results concerning cocharacter-closure for the corresponding G(k)-orbit in V. In the present paper we employ building-theoretic techniques to derive analogous results.

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