{"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}
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Abstract
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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