EuDML | Browse

Let $𝒜$ be a commutative algebraic group defined over a number field $k$ . We consider the following question:Let $r$ be a positive integer and let $P \in 𝒜 (k)$ . Suppose that for all but a finite number of primes $v$ of $k$ , we have $P = r D_{v}$ for some $D_{v} \in 𝒜 (k_{v})$ . Can one conclude that there exists $D \in 𝒜 (k)$ such that $P = r D$ ?A complete answer for the case of the multiplicative group $𝔾_{m}$ is classical. We study other instances and in particular obtain an affirmative answer when $r$ is a prime and $𝒜$ is either an elliptic curve or a torus of small dimension...

Currently displaying 1 – 20 of 31

Page 1 Next

Displaying 1 – 20 of 31

Adhérence d'orbite et invariants.

Algebraic groups with a distinguished conjugacy class.

Cohomology of line bundles on $G / B$

Compléments à l'article «Groupes réductifs»

Correction to “Cohomology of line bundles on $G / B$ ”

Coxeter Orbits and Eigenspaces of Frobenius

Distributions on Toroidal Groups.

Endlich präsentierte arithmetische Gruppen und K2 über Laurent-Polynomringen.

Endliche Hopfalgebren.

Groupes réductifs sur un corps local : I. Données radicielles valuées

Homogene Räume k-affinoider Gruppen.

Invariants symétriques entiers des groupes de Weyl et torsion.

k-affinoide Tor.

Le groupe de Cremona

Local-global divisibility of rational points in some commutative algebraic groups

Lokale und globale Invarianten der Hilbertschen Modulgruppe.

On the congruence subgroup problem

Periods of p-adic Schottky groups.

Picard-Borel-Eigenschaft und Anwendungen.

Rational and Generic Cohomology

Currently displaying 1 – 20 of 31