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Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below Ricci曲率下有界的非坍缩极限空间奇异集的可整流性
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/ANNALS.2021.193.2.2
J. Cheeger, Wenshuai Jiang, A. Naber
{"title":"Rectifiability of singular sets of noncollapsed limit spaces with\u0000 Ricci curvature bounded below","authors":"J. Cheeger, Wenshuai Jiang, A. Naber","doi":"10.4007/ANNALS.2021.193.2.2","DOIUrl":"https://doi.org/10.4007/ANNALS.2021.193.2.2","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 34
The threshold conjecture for the energy critical hyperbolic Yang–Mills equation 能量临界双曲Yang-Mills方程的阈值猜想
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.194.2.1
Oh, Tataru
{"title":"The threshold conjecture for the energy critical hyperbolic\u0000 Yang–Mills equation","authors":"Oh, Tataru","doi":"10.4007/annals.2021.194.2.1","DOIUrl":"https://doi.org/10.4007/annals.2021.194.2.1","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Martin's Maximum++ implies Woodin's axiom (*) 马丁最大值++暗含伍丁公理(*)
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/ANNALS.2021.193.3.3
D. Asperó, R. Schindler
{"title":"Martin's Maximum++ implies Woodin's axiom\u0000 (*)","authors":"D. Asperó, R. Schindler","doi":"10.4007/ANNALS.2021.193.3.3","DOIUrl":"https://doi.org/10.4007/ANNALS.2021.193.3.3","url":null,"abstract":"We show that Martin’s Maximum++ implies Woodin’s Pmax axiom (∗). This answers a question from the 1990’s and amalgamates two prominent axioms of set theory which were both known to imply that there are א2 many real numbers.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
On property (T) for Aut(Fn) and SLn(ℤ) 关于Aut(Fn)和SLn(n)的性质(T)
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.193.2.3
Kaluba, Kielak, Nowak
{"title":"On property (T) for Aut(<em>F<sub>n</sub></em>) and\u0000 SL<sub><em>n</em></sub>(ℤ)","authors":"Kaluba, Kielak, Nowak","doi":"10.4007/annals.2021.193.2.3","DOIUrl":"https://doi.org/10.4007/annals.2021.193.2.3","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strong generators in Dperf(X) and Dbcoh(X) Dperf(X)和Dbcoh(X)中的强生成器
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.193.3.1
Neeman
{"title":"Strong generators in D<sup>perf</sup>(<em>X</em>) and\u0000 D<em><sup>b</sup></em><sub>coh</sub>(<em>X</em>)","authors":"Neeman","doi":"10.4007/annals.2021.193.3.1","DOIUrl":"https://doi.org/10.4007/annals.2021.193.3.1","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Index 指数
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2021-01-01 DOI: 10.4007/annals.2021.193.3.0979
{"title":"Index","authors":"","doi":"10.4007/annals.2021.193.3.0979","DOIUrl":"https://doi.org/10.4007/annals.2021.193.3.0979","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A non-hypergeometric $E$-function 一个非超几何的E函数
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-12-20 DOI: 10.4007/annals.2021.194.3.7
J. Fres'an, P. Jossen
{"title":"A non-hypergeometric $E$-function","authors":"J. Fres'an, P. Jossen","doi":"10.4007/annals.2021.194.3.7","DOIUrl":"https://doi.org/10.4007/annals.2021.194.3.7","url":null,"abstract":"We answer in the negative Siegel’s question whether all E-functions are polynomial expressions in hypergeometric E-functions. Namely, we show that if an irreducible differential operator of order three annihilates an E-function in the hypergeometric class, then the singularities of its Fourier transform are constrained to satisfy a symmetry property that generically does not hold. The proof relies on André’s theory of E-operators and Katz’s computation of the Galois group of hypergeometric differential equations.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44995606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The Chow $t$-structure on the $infty$-category of motivic spectra 动力谱$infty$ -范畴上的Chow $t$ -结构
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-12-04 DOI: 10.4007/annals.2022.195.2.5
Tom Bachmann, Hana Jia Kong, Guozhen Wang, Zhouli Xu
{"title":"The Chow $t$-structure on the $infty$-category of motivic spectra","authors":"Tom Bachmann, Hana Jia Kong, Guozhen Wang, Zhouli Xu","doi":"10.4007/annals.2022.195.2.5","DOIUrl":"https://doi.org/10.4007/annals.2022.195.2.5","url":null,"abstract":"We define the Chow $t$-structure on the $infty$-category of motivic spectra $SH(k)$ over an arbitrary base field $k$. We identify the heart of this $t$-structure $SH(k)^{cheartsuit}$ when the exponential characteristic of $k$ is inverted. Restricting to the cellular subcategory, we identify the Chow heart $SH(k)^{cell, cheartsuit}$ as the category of even graded $MU_{2*}MU$-comodules. Furthermore, we show that the $infty$-category of modules over the Chow truncated sphere spectrum is algebraic. Our results generalize the ones in Gheorghe--Wang--Xu in three aspects: To integral results; To all base fields other than just $C$; To the entire $infty$-category of motivic spectra $SH(k)$, rather than a subcategory containing only certain cellular objects. We also discuss a strategy for computing motivic stable homotopy groups of (p-completed) spheres over an arbitrary base field $k$ using the Postnikov tower associated to the Chow $t$-structure and the motivic Adams spectral sequences over $k$.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47932345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Redshift and multiplication for truncated Brown--Peterson spectra 截断Brown—Peterson谱的红移和乘法
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-12-01 DOI: 10.4007/annals.2022.196.3.6
Jeremy Hahn, D. Wilson
{"title":"Redshift and multiplication for truncated Brown--Peterson spectra","authors":"Jeremy Hahn, D. Wilson","doi":"10.4007/annals.2022.196.3.6","DOIUrl":"https://doi.org/10.4007/annals.2022.196.3.6","url":null,"abstract":"We equip $mathrm{BP} langle n rangle$ with an $mathbb{E}_3$-$mathrm{BP}$-algebra structure, for each prime $p$ and height $n$. The algebraic $K$-theory of this $mathbb{E}_3$-ring is of chromatic height exactly $n+1$.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42022295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 28
On the Brumer--Stark conjecture 关于布鲁默和斯塔克的猜想
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-10-01 DOI: 10.4007/annals.2023.197.1.5
S. Dasgupta, M. Kakde
{"title":"On the Brumer--Stark conjecture","authors":"S. Dasgupta, M. Kakde","doi":"10.4007/annals.2023.197.1.5","DOIUrl":"https://doi.org/10.4007/annals.2023.197.1.5","url":null,"abstract":"Let $H/F$ be a finite abelian extension of number fields with $F$ totally real and $H$ a CM field. Let $S$ and $T$ be disjoint finite sets of places of $F$ satisfying the standard conditions. The Brumer-Stark conjecture states that the Stickelberger element $Theta^{H/F}_{S, T}$ annihilates the $T$-smoothed class group $text{Cl}^T(H)$. We prove this conjecture away from $p=2$, that is, after tensoring with $mathbf{Z}[1/2]$. We prove a stronger version of this result conjectured by Kurihara that gives a formula for the 0th Fitting ideal of the minus part of the Pontryagin dual of $text{Cl}^T(H) otimes mathbf{Z}[1/2]$ in terms of Stickelberger elements. \u0000We also show that this stronger result implies Rubin's higher rank version of the Brumer-Stark conjecture, again away from 2. \u0000Our technique is a generalization of Ribet's method, building upon on our earlier work on the Gross-Stark conjecture. Here we work with group ring valued Hilbert modular forms as introduced by Wiles. A key aspect of our approach is the construction of congruences between cusp forms and Eisenstein series that are stronger than usually expected, arising as shadows of the trivial zeroes of $p$-adic $L$-functions. These stronger congruences are essential to proving that the cohomology classes we construct are unramified at $p$.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45241115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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