Effective diophantine approximation on , II
Effective equidistribution of S-integral points on symmetric varieties
Let be a global field of characteristic not 2. Let be a symmetric variety defined over and a finite set of places of . We obtain counting and equidistribution results for the S-integral points of . Our results are effective when is a number field.
Eigensections on Kuga families of abelian varieties and finiteness of their Mordell-Weil groups.
Ein Analogon des Satzes von Nagell-Lutz über die Torsion einer elliptischen Kurve.
Elliptic Curves: Diophantine Torsion Solutions and Singular j-Invariants.
Elliptic curves with and counterexamples to local-global divisibility by 9
We give a family of elliptic curves, depending on two nonzero rational parameters and , such that the following statement holds: let be an elliptic curve and let be its 3-torsion subgroup. This group verifies if and only if belongs to .Furthermore, we consider the problem of the local-global divisibility by 9 for points of elliptic curves. The number 9 is one of the few exceptional powers of primes, for which an answer to the local-global divisibility is unknown in the case of such...
Elliptic curves with a rational point of finite order.
Elliptic curves with bounded ranks in function field towers
Endlichkeitssätze für abelsche Varietäten über Zahlkörper.
Endlichkeitssätze für abelsche Varietäten über Zahlkörpern.
Endomorphisms of group schemes and rational points on curves
Equations defining rational singularities
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
Errata-Corrige : “The Mordell conjecture revisited”
Erratum : On the Hasse principle for homogeneous spaces with finite stabilizers
Erratum: Rational points of bounded height on Fano varieties. Invent. Math. 95, 421-435 (1989).
Estimation effective des points entiers d'une famille de courbes algébriques
Euclidean algorithm and Kummer covers with many points.
Euclidean rings of affine curves.
Every rational surface is separably split.