The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer.
The defect of weak approximation for homogeneous spaces
Hardy-Littlewood varieties and semisimple groups.
Spherical spaces for which the Hasse principle and weak approximation fail.
We construct spherical homogeneous spaces X of semisimple simply connected groups with connected stabilizers such that the Hasse principle or weak approximation fail for X.
Erratum : On the Hasse principle for homogeneous spaces with finite stabilizers
On the Hasse principle for homogeneous spaces with finite stabilizers
The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme
We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.
Complexes de groupes de type multiplicatif et groupe de Brauer non ramifié des espaces homogènes
On calcule par des méthodes arithmétiques le groupe de Brauer non ramifié des espaces homogènes de groupes algébriques linéaires sur différents corps. Les formules obtenues font intervenir l’hypercohomologie de complexes de groupes de type multiplicatif.
The Hasse principle for homogeneous spaces.
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