Dorota Blinkiewicz

Title: Local to global principle for semiabelian varieties

Abstract:
In this talk, we will present theorem which solves the detecting 
linear dependence problem, with torsion ambiguity, for some family 
of semiabelian varieties G, which are products of tori and abelian 
varieties over number field F and for any finitely generated subgroup H 
of Mordell-Weil group G(F). This result generalizes results of A. Perucca, 
G. Banaszak and P. Krasoń. We will also construct counterexamples 
which show that the basic assumption of this theorem is very important. 
We will also formulate theorem which asserts that it is sufficient to 
consider only finite number of reductions to check whether a point belongs 
to the subgroup (modulo torsion). At the end of this talk we will discuss 
commensurability problem for finitely generated subgroups in Mordell-Weil 
groups of semiabelian varieties.