Cocharacter-closure and spherical buildings

Michael Bate; Sebastian Herpel; Benjamin Martin; Gerhard Rohrle

doi:10.2140/pjm.2015.279.65

Cocharacter-closure and spherical buildings

Michael Bate, Sebastian Herpel, Benjamin Martin, Gerhard Rohrle

Mathematical Science

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

7 Downloads (Pure)

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 language	English
Pages (from-to)	65-85
Number of pages	21
Journal	Pacific Journal of Mathematics
Volume	279
Issue number	1-2
DOIs	https://doi.org/10.2140/pjm.2015.279.65
Publication status	Published - 21 Dec 2015

Keywords

Affine G-variety
cocharacter-closed orbit
rationality
spherical building

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Cocharacter-closure and spherical buildings
First published in ‘Pacific Journal of Mathematics' in Volume 279 Number 1-2, 2015, published by Mathematical Sciences Publishers,” © Copyright 2015 Pacific Journal of Mathematics. All rights reserved.
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T1 - Cocharacter-closure and spherical buildings

AU - Bate, Michael

AU - Herpel, Sebastian

AU - Martin, Benjamin

AU - Rohrle, Gerhard

PY - 2015/12/21

Y1 - 2015/12/21

N2 - 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.

AB - 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.

KW - Affine G-variety

KW - cocharacter-closed orbit

KW - rationality

KW - spherical building

U2 - 10.2140/pjm.2015.279.65

DO - 10.2140/pjm.2015.279.65

M3 - Article

SN - 0030-8730

VL - 279

SP - 65

EP - 85

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1-2

ER -

Cocharacter-closure and spherical buildings

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Keywords

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