TY - JOUR

T1 - Groupe de Picard et groupe de Brauer des compactifications lisses d'espaces homogènes

AU - Colliot-Thélène, Jean Louis

AU - Kunyavskiǐ, Boris È

PY - 2006/10

Y1 - 2006/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33749992587&partnerID=8YFLogxK

U2 - 10.1090/S1056-3911-06-00427-9

DO - 10.1090/S1056-3911-06-00427-9

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33749992587

SN - 1056-3911

VL - 15

SP - 733

EP - 752

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

IS - 4

ER -