{"title":"动机上同的迹形式论","authors":"Tomoyuki Abe","doi":"10.46298/epiga.2023.9742","DOIUrl":null,"url":null,"abstract":"The goal of this paper is to construct trace maps for the six functor\nformalism of motivic cohomology after Voevodsky, Ayoub, and\nCisinski-D\\'{e}glise. We also construct an $\\infty$-enhancement of such a trace\nformalism. In the course of the $\\infty$-enhancement, we need to reinterpret\nthe trace formalism in a more functorial manner. This is done by using\nSuslin-Voevodsky's relative cycle groups.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Trace formalism for motivic cohomology\",\"authors\":\"Tomoyuki Abe\",\"doi\":\"10.46298/epiga.2023.9742\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The goal of this paper is to construct trace maps for the six functor\\nformalism of motivic cohomology after Voevodsky, Ayoub, and\\nCisinski-D\\\\'{e}glise. We also construct an $\\\\infty$-enhancement of such a trace\\nformalism. In the course of the $\\\\infty$-enhancement, we need to reinterpret\\nthe trace formalism in a more functorial manner. This is done by using\\nSuslin-Voevodsky's relative cycle groups.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/epiga.2023.9742\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2023.9742","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The goal of this paper is to construct trace maps for the six functor
formalism of motivic cohomology after Voevodsky, Ayoub, and
Cisinski-D\'{e}glise. We also construct an $\infty$-enhancement of such a trace
formalism. In the course of the $\infty$-enhancement, we need to reinterpret
the trace formalism in a more functorial manner. This is done by using
Suslin-Voevodsky's relative cycle groups.
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