Cartier modules and cyclotomic spectra

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2018-09-05 DOI:10.1090/jams/951

Benjamin Antieau, T. Nikolaus

{"title":"Cartier modules and cyclotomic spectra","authors":"Benjamin Antieau, T. Nikolaus","doi":"10.1090/jams/951","DOIUrl":null,"url":null,"abstract":"<p>We construct and study a <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t\">\n <mml:semantics>\n <mml:mi>t</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">t</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-structure on <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\n <mml:semantics>\n <mml:mi>p</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t\">\n <mml:semantics>\n <mml:mi>t</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">t</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-structure. Our main tool is a new approach to <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\n <mml:semantics>\n <mml:mi>p</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-typical cyclotomic spectra via objects we call <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\n <mml:semantics>\n <mml:mi>p</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-typical topological Cartier modules. Using these, we prove that the heart of the cyclotomic <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t\">\n <mml:semantics>\n <mml:mi>t</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">t</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-structure is the full subcategory of derived <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\">\n <mml:semantics>\n <mml:mi>V</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">V</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-complete objects in the abelian category of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\n <mml:semantics>\n <mml:mi>p</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>-typical Cartier modules.</p>","PeriodicalId":54764,"journal":{"name":"Journal of the American Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2018-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jams/951","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 18

Abstract

We construct and study a t t -structure on p p -typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this t t -structure. Our main tool is a new approach to p p -typical cyclotomic spectra via objects we call p p -typical topological Cartier modules. Using these, we prove that the heart of the cyclotomic t t -structure is the full subcategory of derived V V -complete objects in the abelian category of p p -typical Cartier modules.

查看原文本刊更多论文

卡地亚模组与旋光光谱

我们构造并研究了p-p典型分原子谱上的一个t-结构，并解释了如何利用该t-结构恢复完美场上光滑方案的晶体上同调。我们的主要工具是通过我们称之为p-典型拓扑卡地亚模的对象来获得p-典型分圆光谱的新方法。利用这些，我们证明了分圆t-结构的中心是p-典型Cartier模的阿贝尔范畴中导出的V-V-完全对象的全子范畴。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.