Geometry-of-numbers methods are extended to count orbits in coregular spaces over arbitrary global fields, yielding bounds on average ranks and Selmer sizes for elliptic curves and hyperelliptic Jacobians.
Bhargava, Most hyperelliptic overQcurves have no rational points,http://arxiv.org/abs/ 1308.0395
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Geometry-of-numbers methods over global fields II: Coregular representations
Geometry-of-numbers methods are extended to count orbits in coregular spaces over arbitrary global fields, yielding bounds on average ranks and Selmer sizes for elliptic curves and hyperelliptic Jacobians.