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arXiv · 1811.00966

The geometric average size of Selmer groups over function fields

Aaron Landesman
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Abstract

We show, in the large $q$ limit, that the average size of $n$-Selmer groups of elliptic curves of bounded height over $\mathbb F_q(t)$ is the sum of the divisors of $n$. As a corollary, again in the large $q$ limit, we deduce that $100\%$ of elliptic curves of bounded height over $\mathbb F_q(t)$ have rank $0$ or $1$.

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Aaron Landesman. 2018-11-02. The geometric average size of Selmer groups over function fields. https://doi.org/10.2140/ant.2021.15.673

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