{"title":"Motivic invariants of birational maps | Annals of Mathematics","authors":"Hsueh-Yung Lin, Evgeny Shinder","doi":"10.4007/annals.2024.199.1.6","DOIUrl":null,"url":null,"abstract":"<p>We construct invariants of birational maps with values in the Kontsevich–Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are well-suited to investigating the structure of the Grothendieck ring and L-equivalence. Building on known constructions of L-equivalence, we prove new unexpected results about Cremona groups.</p>","PeriodicalId":5,"journal":{"name":"ACS Applied Materials & Interfaces","volume":null,"pages":null},"PeriodicalIF":8.3000,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Materials & Interfaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4007/annals.2024.199.1.6","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We construct invariants of birational maps with values in the Kontsevich–Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are well-suited to investigating the structure of the Grothendieck ring and L-equivalence. Building on known constructions of L-equivalence, we prove new unexpected results about Cremona groups.
期刊介绍：
ACS Applied Materials & Interfaces is a leading interdisciplinary journal that brings together chemists, engineers, physicists, and biologists to explore the development and utilization of newly-discovered materials and interfacial processes for specific applications. Our journal has experienced remarkable growth since its establishment in 2009, both in terms of the number of articles published and the impact of the research showcased. We are proud to foster a truly global community, with the majority of published articles originating from outside the United States, reflecting the rapid growth of applied research worldwide.
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