Vol. 319, No. 2, 2022

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Average size of 2-Selmer groups of Jacobians of odd hyperelliptic curves over function fields

Dao Van Thinh

Vol. 319 (2022), No. 2, 259–305
Abstract

We compute the average size of 2-Selmer groups of the family of hyperelliptic curves with a marked Weierstrass point over function fields. The result is obtained by a geometric method which could be considered as a generalization of the one that was used previously by Q. P. Ho, V. B. Le Hung, and B. C. Ngo (Math. Res. Lett. 21:6 (2014), 1305–1339) to obtain the average size of 2-Selmer groups of elliptic curves.

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Keywords
2-Selmer group, hyperelliptic curve, function field
Mathematical Subject Classification
Primary: 11G30, 14H40
Milestones
Received: 19 January 2019
Revised: 16 March 2021
Accepted: 9 February 2022
Published: 11 September 2022
Authors
Dao Van Thinh
Peking University
Beijing
China