{"title":"正特征 I 中的$textbf{GL}$$-代数：外部代数","authors":"Karthik Ganapathy","doi":"10.1007/s00029-024-00960-4","DOIUrl":null,"url":null,"abstract":"<p>We study the category of <span>\\(\\textbf{GL}\\)</span>-equivariant modules over the infinite exterior algebra in positive characteristic. Our main structural result is a shift theorem à la Nagpal. Using this, we obtain a Church–Ellenberg type bound for the Castelnuovo–Mumford regularity. We also prove finiteness results for local cohomology.</p>","PeriodicalId":501600,"journal":{"name":"Selecta Mathematica","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$$\\\\textbf{GL}$$ -algebras in positive characteristic I: the exterior algebra\",\"authors\":\"Karthik Ganapathy\",\"doi\":\"10.1007/s00029-024-00960-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study the category of <span>\\\\(\\\\textbf{GL}\\\\)</span>-equivariant modules over the infinite exterior algebra in positive characteristic. Our main structural result is a shift theorem à la Nagpal. Using this, we obtain a Church–Ellenberg type bound for the Castelnuovo–Mumford regularity. We also prove finiteness results for local cohomology.</p>\",\"PeriodicalId\":501600,\"journal\":{\"name\":\"Selecta Mathematica\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Selecta Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00029-024-00960-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Selecta Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00029-024-00960-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
$$\textbf{GL}$$ -algebras in positive characteristic I: the exterior algebra
We study the category of \(\textbf{GL}\)-equivariant modules over the infinite exterior algebra in positive characteristic. Our main structural result is a shift theorem à la Nagpal. Using this, we obtain a Church–Ellenberg type bound for the Castelnuovo–Mumford regularity. We also prove finiteness results for local cohomology.
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