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.
Laga, The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3, Algebr
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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.