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2021 The geometric average size of Selmer groups over function fields
Aaron Landesman
Algebra Number Theory 15(3): 673-709 (2021). DOI: 10.2140/ant.2021.15.673

Abstract

We show, in the large q limit, that the average size of n-Selmer groups of elliptic curves of bounded height over 𝔽q(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 𝔽q(t) have rank 0 or 1.

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Aaron Landesman. "The geometric average size of Selmer groups over function fields." Algebra Number Theory 15 (3) 673 - 709, 2021. https://doi.org/10.2140/ant.2021.15.673

Information

Received: 5 August 2019; Revised: 5 July 2020; Accepted: 7 September 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.673

Subjects:
Primary: 11G05

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 3 • 2021
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