{"title":"重新参观德·拉姆-维特建筑群","authors":"B. Bhatt, J. Lurie, A. Mathew","doi":"10.24033/ast.1146","DOIUrl":null,"url":null,"abstract":"The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p$. \nWe introduce a category of cochain complexes equipped with an endomorphism $F$ (of underlying graded abelian groups) satisfying $dF = pFd$, whose homological algebra we study in detail. To any such object satisfying an abstract analog of the Cartier isomorphism, an elementary homological process associates a generalization of the de Rham-Witt construction. Abstractly, the homological algebra can be viewed as a calculation of the fixed points of the Berthelot-Ogus operator $L \\eta_p$ on the $p$-complete derived category. We give various applications of this approach, including a simplification of the crystalline comparison in $A \\Omega$-cohomology theory.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":" ","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2018-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":"{\"title\":\"Revisiting the de Rham-Witt complex\",\"authors\":\"B. Bhatt, J. Lurie, A. Mathew\",\"doi\":\"10.24033/ast.1146\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p$. \\nWe introduce a category of cochain complexes equipped with an endomorphism $F$ (of underlying graded abelian groups) satisfying $dF = pFd$, whose homological algebra we study in detail. To any such object satisfying an abstract analog of the Cartier isomorphism, an elementary homological process associates a generalization of the de Rham-Witt construction. Abstractly, the homological algebra can be viewed as a calculation of the fixed points of the Berthelot-Ogus operator $L \\\\eta_p$ on the $p$-complete derived category. We give various applications of this approach, including a simplification of the crystalline comparison in $A \\\\Omega$-cohomology theory.\",\"PeriodicalId\":55445,\"journal\":{\"name\":\"Asterisque\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2018-05-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asterisque\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.24033/ast.1146\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asterisque","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ast.1146","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p$.
We introduce a category of cochain complexes equipped with an endomorphism $F$ (of underlying graded abelian groups) satisfying $dF = pFd$, whose homological algebra we study in detail. To any such object satisfying an abstract analog of the Cartier isomorphism, an elementary homological process associates a generalization of the de Rham-Witt construction. Abstractly, the homological algebra can be viewed as a calculation of the fixed points of the Berthelot-Ogus operator $L \eta_p$ on the $p$-complete derived category. We give various applications of this approach, including a simplification of the crystalline comparison in $A \Omega$-cohomology theory.
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