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4 papers · 1 filter
Abstract intersection theory and operators in Hilbert space
Grzegorz Banaszak, Yoichi Uetake
For an operator of a certain class in Hilbert space, we introduce axioms of an abstract intersection theory, which we prove to be equivalent to the Riemann Hypothesis concerning th…
On a generalization of the support problem of Erdos and its analogues for abelian varieties and K-theory
Stefan Barańczuk
In this paper we consider certain local-global principles for Mordell-Weil type groups over number fields like S-units, abelian varieties and algebraic K-theory groups
On a Hasse principle for Mordell-Weil groups
Grzegorz Banaszak
In this paper we establish a Hasse principle concerning the linear dependence over of nontorsion points in the Mordell-Weil group of an abelian variety over a number field.
Detecting linear dependence by reduction maps
Grzegorz Banaszak, Wojciech Gajda, Piotr Krason
We consider the local to global principle for detecting linear dependence of points in groups of the Mordell-Weil type. As applications of our general setting we obtain correspondi…