Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Groupe de Picard et groupe de Brauer des compactifications lisses d'espaces homogènes


Authors: Jean-Louis Colliot-Thélène and Boris È. Kunyavskii
Journal: J. Algebraic Geom. 15 (2006), 733-752
DOI: https://doi.org/10.1090/S1056-3911-06-00427-9
Published electronically: June 12, 2006
MathSciNet review: 2237268
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Abstract | References | Additional Information

Abstract: Let $ k$ be a field of characteristic zero, $ G$ a connected linear algebraic group over $ k$ and $ H$ a connected closed $ k$-subgroup of $ G$. Let $ X$ be a smooth $ k$-compactification of $ Y=G/H$. We prove that the Galois lattice given by the geometric Picard group of $ X$ is flasque. The result was known in the case $ H=1$. We compute this Galois lattice up to addition of a permutation module. When $ G$ is semisimple and simply connected, the result shows that the Brauer group of $ X$ is determined by the maximal toric quotient of $ H$.


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Jean-Louis Colliot-Thélène
Affiliation: C.N.R.S., UMR 8628, Mathématiques, Bâtiment 425, Université de Paris-Sud, F-91405 Orsay, France
Email: colliot@math.u-psud.fr

Boris È. Kunyavskii
Affiliation: Bar-Ilan University, Department of Mathematics, 52900 Ramat Gan, Israel
Email: kunyav@macs.biu.ac.il

DOI: https://doi.org/10.1090/S1056-3911-06-00427-9
Received by editor(s): March 26, 2005
Received by editor(s) in revised form: April 21, 2005, and June 23, 2005
Published electronically: June 12, 2006

American Mathematical Society