2^∞-Selmer Rank Parities via the Prym Construction

2021/08/21 by Jordan Docking, Docking, Jordan
Computer Science · Mathematics · #11G30 #11G40 (Primary) 11G10 #14G10 #14H10 #14H45 #14K15 (Secondary) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2108.09564

openalex publication_date 2021/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a local formula for the parity of the 2^∞-Selmer rank of Jacobians of curves of genus 2 or 3 with a K-rational 2-torsion point. We give an explicit example to show how this local formula gives rank parity predictions against which the 2-parity conjecture may be tested. Our results yield applications to the parity conjecture for semistable curves of genus 3.

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