In this paper we consider orders of images of nontorsion points by reduction maps for abelian varieties defined over number fields and for odd dimensional K-groups of number fields. As an application we obtain the generalization of the support problem for abelian varieties and K-groups.
In this paper we consider reduction of nontorsion elements in the étale and Quillen K-theory of a curve X over a number field. As an application we solve two problems: detecting linear dependence and the support problem.
We analyse the number eld-theoretic properties of solutions of the eigenproblem of the Heisenberg Hamiltonian for the magnetic hexagon with the single-node spin 1/2 and isotropic exchange interactions. It follows that eigenenergies and eigenstates are expressible within an extension of the prime eld Q of rationals of degree 2 3 and 2 4 , respectively. In quantum information setting, each real extension of rank 2 represents an arithmetic qubit. We demonstrate in detail some actions of the Galois group on the eigenproblem.
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