2∞-Selmer rank parities via the Prym construction

被引：0
|
作者：
Docking, Jordan [1 ]
机构：
[1] UCL, London, England
来源：
JOURNAL OF NUMBER THEORY | 2024年 / 265卷
关键词：
Prym varieties; Jacobians; Ranks; Parity conjecture; Genus; 2; curves; 3; ELLIPTIC-CURVES; VARIETIES;
D O I：
10.1016/j.jnt.2024.06.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We derive a local formula for the parity of the 2 infinity-Selmer infinity-Selmer rank of Jacobians of curves of genus 2 or 3 which admit an unramified double cover. 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. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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页码：208 / 225
页数：18
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