{"title":"关于有理动同伦范畴","authors":"F. D'eglise, J. Fasel, Adeel A. Khan, F. Jin","doi":"10.5802/JEP.153","DOIUrl":null,"url":null,"abstract":"We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity, stability of constructible objects, and Grothendieck-Verdier duality for SH_Q. Next, we prove that SH_Q is canonically SL-oriented; we compare SH_Q with the category of rational Milnor-Witt motives; and we relate the rational bivariant A^1-theory to Chow-Witt groups. These results are derived from analogous statements for the minus part of SH[1/2].","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"On the rational motivic homotopy category\",\"authors\":\"F. D'eglise, J. Fasel, Adeel A. Khan, F. Jin\",\"doi\":\"10.5802/JEP.153\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity, stability of constructible objects, and Grothendieck-Verdier duality for SH_Q. Next, we prove that SH_Q is canonically SL-oriented; we compare SH_Q with the category of rational Milnor-Witt motives; and we relate the rational bivariant A^1-theory to Chow-Witt groups. These results are derived from analogous statements for the minus part of SH[1/2].\",\"PeriodicalId\":106406,\"journal\":{\"name\":\"Journal de l’École polytechnique — Mathématiques\",\"volume\":\"51 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal de l’École polytechnique — Mathématiques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/JEP.153\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de l’École polytechnique — Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/JEP.153","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity, stability of constructible objects, and Grothendieck-Verdier duality for SH_Q. Next, we prove that SH_Q is canonically SL-oriented; we compare SH_Q with the category of rational Milnor-Witt motives; and we relate the rational bivariant A^1-theory to Chow-Witt groups. These results are derived from analogous statements for the minus part of SH[1/2].
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