{"title":"准阿贝尔变体上的符号卷积","authors":"Jakob Bergqvist, Thuong Dang, Stefan Schröer","doi":"10.1016/j.indag.2024.04.006","DOIUrl":null,"url":null,"abstract":"<div><p>We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil–Châtelet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is étale and contains no points of finite order. In dimension one, such quotients are Brauer–Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces.</p></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"35 3","pages":"Pages 570-583"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357724000387/pdfft?md5=204d239f9d696a1e77d8dd327376fb09&pid=1-s2.0-S0019357724000387-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Sign involutions on para-abelian varieties\",\"authors\":\"Jakob Bergqvist, Thuong Dang, Stefan Schröer\",\"doi\":\"10.1016/j.indag.2024.04.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil–Châtelet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is étale and contains no points of finite order. In dimension one, such quotients are Brauer–Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces.</p></div>\",\"PeriodicalId\":56126,\"journal\":{\"name\":\"Indagationes Mathematicae-New Series\",\"volume\":\"35 3\",\"pages\":\"Pages 570-583\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0019357724000387/pdfft?md5=204d239f9d696a1e77d8dd327376fb09&pid=1-s2.0-S0019357724000387-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae-New Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019357724000387\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/5/3 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae-New Series","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357724000387","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/5/3 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil–Châtelet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is étale and contains no points of finite order. In dimension one, such quotients are Brauer–Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces.
期刊介绍：
Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.
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