{"title":"通过普赖姆构造的 2∞ 塞尔默秩奇偶性","authors":"Jordan Docking","doi":"10.1016/j.jnt.2024.06.009","DOIUrl":null,"url":null,"abstract":"<div><p>We derive a local formula for the parity of the <span><math><msup><mrow><mn>2</mn></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-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.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022314X24001525/pdfft?md5=19533e2a3ab48597f61bd70dc3f8df28&pid=1-s2.0-S0022314X24001525-main.pdf","citationCount":"0","resultStr":"{\"title\":\"2∞-Selmer rank parities via the Prym construction\",\"authors\":\"Jordan Docking\",\"doi\":\"10.1016/j.jnt.2024.06.009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We derive a local formula for the parity of the <span><math><msup><mrow><mn>2</mn></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-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.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001525/pdfft?md5=19533e2a3ab48597f61bd70dc3f8df28&pid=1-s2.0-S0022314X24001525-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001525\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24001525","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We derive a local formula for the parity of the -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.