Jean-Louis Colliot-Thélène Alexei N. Skorobogatov Page 1 The Brauer– Grothendieck Group
Jean-Louis Colliot-Thélène Alexei N. Skorobogatov Ergebnisse der Mathematik und ihrer …

An integer may be represented by a quadratic form over each ring of p-adic integers and
over the reals without being represented by this quadratic form over the integers. More …

Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over
number fields were proposed by Colliot-Thélène, Sansuc, Kato and Saito in the 1980's. We …

We conjecture that the exceptional set in Manin's conjecture has an explicit geometric
description. Our proposal includes the rational point contributions from any generically finite …

For a homogeneous spaceX (not necessarily principal) of a connected algebraic group G
(not necessarily linear) over a number field k, we prove a theorem of strong approximation …

Soit $ X $ une compactification lisse d'un espace homogène d'un groupe algébrique linéaire
$ G $ sur un corps de nombres $ k $. Nous établissons la conjecture de Colliot-Thélène …

Non-abelian Cohomology and Rational Points Page 1 Non-abelian Cohomology and Rational
Points DAVID HARARI1 and ALEXEI N. SKOROBOGATOV2 1DMA, ENS, 45 rue d’Ulm, 75005 …

We report on progress in the qualitative study of rational points on rationally connected
varieties over number fields, also examining integral points, zero-cycles, and non-rationally …

In this paper we prove local–global principles for the existence of an embedding (E, σ)↪(A,
τ) of a given global field E endowed with an involutive automorphism σ into a simple algebra …

Let k be a field of characteristic zero, and let k ̲ be an algebraic closure of k. For a
geometrically integral variety X over k, we write k ̲ (X) for the function field of X ̲= X× kk ̲ …