{"title":"Blow-up invariance of cohomology theories with modulus","authors":"Junnosuke Koizumi","doi":"10.1016/j.aim.2024.109967","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study cohomology theories of <span><math><mi>Q</mi></math></span>-modulus pairs, which are pairs <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> consisting of a scheme <em>X</em> and a <span><math><mi>Q</mi></math></span>-divisor <em>D</em>. Our main theorem provides a sufficient condition for such a cohomology theory to be invariant under blow-ups with centers contained in the divisor. This yields a short proof of the blow-up invariance of the Hodge cohomology with modulus proved by Kelly-Miyazaki. We also define the Witt vector cohomology with modulus using the Brylinski-Kato filtration and prove its blow-up invariance.</div></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824004821","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study cohomology theories of -modulus pairs, which are pairs consisting of a scheme X and a -divisor D. Our main theorem provides a sufficient condition for such a cohomology theory to be invariant under blow-ups with centers contained in the divisor. This yields a short proof of the blow-up invariance of the Hodge cohomology with modulus proved by Kelly-Miyazaki. We also define the Witt vector cohomology with modulus using the Brylinski-Kato filtration and prove its blow-up invariance.
本文研究 Q 模对的同调理论，即由方案 X 和 Q 分因子 D 组成的对 (X,D)。我们的主要定理提供了一个充分条件，使这种同调理论在中心包含在分因子中的吹胀下保持不变。这就产生了凯利-宫崎（Kelly-Miyazaki）所证明的带模霍奇同调的炸毁不变性的简短证明。我们还利用布赖林斯基-加藤滤波定义了带模的维特向量同调，并证明了它的炸毁不变性。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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