Almost ℂp Galois representations and vector bundles

IF 0.8 Q2 MATHEMATICS
J. Fontaine
{"title":"Almost ℂp Galois representations and vector\nbundles","authors":"J. Fontaine","doi":"10.2140/tunis.2020.2.667","DOIUrl":null,"url":null,"abstract":"Let $K$ be a finite extension of $\\mathbb{Q}_p$ and $G_K$ the absolute Galois group. Then $G_K$ acts on the fundamental curve $X$ of $p$-adic Hodge theory and we may consider the abelian category $\\mathcal{M}(G_K)$ of coherent $\\mathcal{O}_X$-modules equipped with a continuous and semi-linear action of $G_K$. An almost $C_p$-representation of $G_K$ is a $p$-adic Banach space $V$ equipped with a linear and continuous action of $G_K$ such that there exists $d\\in\\mathbb{N}$, two $G_K$-stable finite dimensional sub-$\\mathbb{Q}_p$-vector spaces $U_+$ of $V$, $U_-$ of $C_p^d$, and a $G_K$-equivariant isomorphism $V/U_+\\to C_p^d/U_-$. These representations form an abelian category $\\mathcal{C}(G_K)$. The main purpose of this paper is to prove that $\\mathcal{C}(G_K)$ can be recovered from $\\mathcal{M}(G_K)$ by a simple construction (and conversely) inducing, in particular, an equivalence of triangulated categories $D^b(\\mathcal{M}(G_K))\\to D^b(\\mathcal{C}(G_K))$.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2018-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/tunis.2020.2.667","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tunisian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/tunis.2020.2.667","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2

Abstract

Let $K$ be a finite extension of $\mathbb{Q}_p$ and $G_K$ the absolute Galois group. Then $G_K$ acts on the fundamental curve $X$ of $p$-adic Hodge theory and we may consider the abelian category $\mathcal{M}(G_K)$ of coherent $\mathcal{O}_X$-modules equipped with a continuous and semi-linear action of $G_K$. An almost $C_p$-representation of $G_K$ is a $p$-adic Banach space $V$ equipped with a linear and continuous action of $G_K$ such that there exists $d\in\mathbb{N}$, two $G_K$-stable finite dimensional sub-$\mathbb{Q}_p$-vector spaces $U_+$ of $V$, $U_-$ of $C_p^d$, and a $G_K$-equivariant isomorphism $V/U_+\to C_p^d/U_-$. These representations form an abelian category $\mathcal{C}(G_K)$. The main purpose of this paper is to prove that $\mathcal{C}(G_K)$ can be recovered from $\mathcal{M}(G_K)$ by a simple construction (and conversely) inducing, in particular, an equivalence of triangulated categories $D^b(\mathcal{M}(G_K))\to D^b(\mathcal{C}(G_K))$.
几乎ℂp Galois表示和向量丛
设$K$是$\mathbb的有限扩展{Q}_p$和$G_K$是绝对伽罗瓦群。然后$G_K$作用于$p$-adic-Hodge理论的基本曲线$X$,我们可以考虑相干$\mathcal的阿贝尔范畴$\mathcal{M}(G_K)${O}_X$-模块,配备有$G_K$的连续和半线性动作。$G_K$的一个几乎$C_p$-表示是一个$p$adic Banach空间$V$,它配备了$G_K$d的线性连续作用,使得存在$d\in\mathbb{N}$,两个$G_K$2稳定的有限维子$\mathbb{Q}_p$V$的$U_+$向量空间,$C_p^d$的$U-$向量空间和C_p^d/U_-$的$G_K$等变同构$V/U_+\。这些表示形成了一个阿贝尔范畴$\mathcal{C}(G_K)$。本文的主要目的是证明$\mathcal{C}(G_K)$可以通过一个简单的构造(反之亦然)从$\mathical{M}(G_K)$中恢复,特别是通过导出三角范畴$D^b(\mathcal{M}。
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
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信