{"title":"A note on local formulae for the parity of Selmer ranks","authors":"Adam Morgan","doi":"arxiv-2409.08034","DOIUrl":null,"url":null,"abstract":"In this note, we provide evidence for a certain twisted version of the parity\nconjecture for Jacobians, introduced in prior work of V. Dokchitser, Green,\nKonstantinou and the author. To do this, we use arithmetic duality theorems for\nabelian varieties to study the determinant of certain endomorphisms acting on\np-infinity Selmer groups.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08034","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we provide evidence for a certain twisted version of the parity
conjecture for Jacobians, introduced in prior work of V. Dokchitser, Green,
Konstantinou and the author. To do this, we use arithmetic duality theorems for
abelian varieties to study the determinant of certain endomorphisms acting on
p-infinity Selmer groups.
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