夯素上一些单元式志村变的半可变模型

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-09-19 DOI:10.2140/ant.2024.18.1715

Ioannis Zachos

{"title":"夯素上一些单元式志村变的半可变模型","authors":"Ioannis Zachos","doi":"10.2140/ant.2024.18.1715","DOIUrl":null,"url":null,"abstract":"<p>We consider Shimura varieties associated to a unitary group of signature <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><mi>n</mi>\n<mo>−</mo> <mn>2</mn><mo>,</mo><mn>2</mn><mo stretchy=\"false\">)</mo></math>. We give regular <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math>-adic integral models for these varieties over odd primes <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math> which ramify in the imaginary quadratic field with level subgroup at <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math> given by the stabilizer of a selfdual lattice in the hermitian space. Our construction is given by an explicit resolution of a corresponding local model. </p>","PeriodicalId":50828,"journal":{"name":"Algebra & Number Theory","volume":"197 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semistable models for some unitary Shimura varieties over ramified primes\",\"authors\":\"Ioannis Zachos\",\"doi\":\"10.2140/ant.2024.18.1715\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider Shimura varieties associated to a unitary group of signature <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mo stretchy=\\\"false\\\">(</mo><mi>n</mi>\\n<mo>−</mo> <mn>2</mn><mo>,</mo><mn>2</mn><mo stretchy=\\\"false\\\">)</mo></math>. We give regular <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>p</mi></math>-adic integral models for these varieties over odd primes <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>p</mi></math> which ramify in the imaginary quadratic field with level subgroup at <math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>p</mi></math> given by the stabilizer of a selfdual lattice in the hermitian space. Our construction is given by an explicit resolution of a corresponding local model. </p>\",\"PeriodicalId\":50828,\"journal\":{\"name\":\"Algebra & Number Theory\",\"volume\":\"197 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra & Number Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/ant.2024.18.1715\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Number Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/ant.2024.18.1715","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑的是与签名为 (n- 2,2) 的单元群相关联的志村变项。我们给出了这些奇数素数 p 上的正规 p-adic 积分模型，这些模型在虚二次域中发生斜伸，其 p 处的水平子群由赫米提空间中自偶晶格的稳定子给出。我们的构造由相应局部模型的明确解析给出。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Semistable models for some unitary Shimura varieties over ramified primes

We consider Shimura varieties associated to a unitary group of signature $(n - 2, 2)$ . We give regular $p$ -adic integral models for these varieties over odd primes $p$ which ramify in the imaginary quadratic field with level subgroup at $p$ given by the stabilizer of a selfdual lattice in the hermitian space. Our construction is given by an explicit resolution of a corresponding local model.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.