On albanese torsors and the elementary obstruction
TLDR
In this paper, it was shown that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X, over an arbitrary field, can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X.Abstract:
We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X, over an arbitrary field, can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X. Arithmetic applications are given.read more
Citations
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Journal ArticleDOI
Arithmetic duality theorems
TL;DR: The complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry can be found in this paper, where the authors provide a good introduction to the subject.
OtherDOI
Some structure theorems for algebraic groups
TL;DR: In this article, the authors present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism groups, and present extended notes of a course given at Tulane University for the 2015 Clifford Lectures.
Journal ArticleDOI
The elementary obstruction and homogeneous spaces
TL;DR: In this article, Brauer et al. consider a k-variete X geometriquement integre, on note k(X) le corps des fonctions de X=X×kk, where X possede un k-point lisse, le plongement naturel de groupes multiplicatifs k*↪k(X)* admet une retraction equivariante for l'action du groupe de Galois de k sur k.
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Anti-affine algebraic groups
TL;DR: In this paper, it was shown that an algebraic group G over a field is anti-affine if every regular function on G is constant, and a classification of these groups was obtained, with applications to the structure of algebraic groups in positive characteristics.
References
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Book
Éléments de géométrie algébrique
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Book
Rational Curves on Algebraic Varieties
TL;DR: It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.