Cocharacter-closure and spherical buildings

Michael Bate, Sebastian Herpel, Benjamin Martin, Gerhard Rohrle

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Abstract

Let kk be a field, let GG be a reductive kk-group and VV an affine kk-variety on which GG acts. In this note we continue our study of the notion of cocharacter-closed G(k)G(k)-orbits in VV. In earlier work we used a rationality condition on the point stabilizer of a GG-orbit to prove Galois ascent/descent and Levi ascent/descent results concerning cocharacter-closure for the corresponding G(k)G(k)-orbit in VV. In the present paper we employ building-theoretic techniques to derive analogous results.
Original languageEnglish
Pages (from-to)65-85
Number of pages21
Journal Pacific Journal of Mathematics
Volume279
Issue number1-2
DOIs
Publication statusPublished - 21 Dec 2015

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Keywords

  • Affine G-variety
  • cocharacter-closed orbit
  • rationality
  • spherical building

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