{"title":"(通过固化的（半）拓扑 $K$ 理论","authors":"Ko Aoki","doi":"arxiv-2409.01462","DOIUrl":null,"url":null,"abstract":"Clausen--Scholze introduced the notion of solid spectrum in their condensed\nmathematics program. We demonstrate that the solidification of algebraic\n$K$-theory recovers two known constructions: the semitopological $K$-theory of\na real (associative) algebra and the topological (aka operator) $K$-theory of a\nreal Banach algebra.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"75 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"(Semi)topological $K$-theory via solidification\",\"authors\":\"Ko Aoki\",\"doi\":\"arxiv-2409.01462\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Clausen--Scholze introduced the notion of solid spectrum in their condensed\\nmathematics program. We demonstrate that the solidification of algebraic\\n$K$-theory recovers two known constructions: the semitopological $K$-theory of\\na real (associative) algebra and the topological (aka operator) $K$-theory of a\\nreal Banach algebra.\",\"PeriodicalId\":501136,\"journal\":{\"name\":\"arXiv - MATH - Rings and Algebras\",\"volume\":\"75 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Rings and Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.01462\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.01462","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Clausen--Scholze introduced the notion of solid spectrum in their condensed
mathematics program. We demonstrate that the solidification of algebraic
$K$-theory recovers two known constructions: the semitopological $K$-theory of
a real (associative) algebra and the topological (aka operator) $K$-theory of a
real Banach algebra.
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