On the Artin vanishing theorem for Stein spaces

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-07-01 DOI:10.1112/blms.70124

Olivier Benoist

{"title":"On the Artin vanishing theorem for Stein spaces","authors":"Olivier Benoist","doi":"10.1112/blms.70124","DOIUrl":null,"url":null,"abstract":"Artin vanishing theorems for Stein spaces refer to the vanishing of some of their (co)homology groups in degrees higher than the dimension. We obtain new positive and negative results concerning Artin vanishing for the cohomology of a Stein space relative to a Runge open subset. We also prove an Artin vanishing theorem for the <math>\n <semantics>\n <mrow>\n <mi>Gal</mi>\n <mo>(</mo>\n <mi>C</mi>\n <mo>/</mo>\n <mi>R</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathrm{Gal}(\\mathbb {C}/\\mathbb {R})$</annotation>\n </semantics></math>-equivariant cohomology of a <math>\n <semantics>\n <mrow>\n <mi>Gal</mi>\n <mo>(</mo>\n <mi>C</mi>\n <mo>/</mo>\n <mi>R</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathrm{Gal}(\\mathbb {C}/\\mathbb {R})$</annotation>\n </semantics></math>-equivariant Stein space relative to the fixed locus.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2757-2769"},"PeriodicalIF":0.9000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/blms.70124","RegionNum":3,"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

Abstract

Artin vanishing theorems for Stein spaces refer to the vanishing of some of their (co)homology groups in degrees higher than the dimension. We obtain new positive and negative results concerning Artin vanishing for the cohomology of a Stein space relative to a Runge open subset. We also prove an Artin vanishing theorem for the $Gal (C / R)$ -equivariant cohomology of a $Gal (C / R)$ -equivariant Stein space relative to the fixed locus.

Abstract Image

查看原文本刊更多论文

关于Stein空间的Artin消失定理

Stein空间的Artin消失定理是指其（co）同调群在高于维数的度上的消失。我们得到了Stein空间相对于Runge开子集上同调的Artin消失的新的正负结果。我们还证明了Gal (C / R)$ \ mathm {Gal}(\mathbb {C}/\mathbb {R})$ - Gal (C / R)$ \ mathm {Gal}(\mathbb})$的等变上同调的Artin消失定理{C}/\mathbb {R})$ -相对于固定轨迹的等变斯坦空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊