AbstractThe shrinking target problem concerns the sizes of the sets of the points in a metric space whose orbits under a transformation fall into a family of shrinking subsets infinitely often. We study such problems for matrices with real coefficients which are transformations on the d-dimensional torus. We obtain a zero-one law for the Lebesgue measure of the corresponding shrinking target se...
AbstractThe classical Hodge conjecture states that for a smooth projective variety any rational (p,p)-class can be represented by an algebraic cycle. The first non-trivial case for abelian varietie
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