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Keel's base point free theorem and quotients in mixed characteristic 混合特征中的Keel无基点定理和商
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-02-27 DOI: 10.4007/annals.2022.195.2.4
J. Witaszek
{"title":"Keel's base point free theorem and quotients in mixed characteristic","authors":"J. Witaszek","doi":"10.4007/annals.2022.195.2.4","DOIUrl":"https://doi.org/10.4007/annals.2022.195.2.4","url":null,"abstract":"We develop techniques of mimicking the Frobenius action in the study of universal homeomorphisms in mixed characteristic. As a consequence, we show a mixed characteristic Keel's base point free theorem obtaining applications towards the mixed characteristic Minimal Model Program, we generalise Kollar's theorem on the existence of quotients by finite equivalence relations to mixed characteristic, and we provide a new proof of the existence of quotients by affine group schemes.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42773230","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: 13
Uniformity in Mordell–Lang for curves 曲线的Mordell–Lang一致性
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-01-28 DOI: 10.4007/annals.2021.194.1.4
V. Dimitrov, Ziyang Gao, P. Habegger
{"title":"Uniformity in Mordell–Lang for curves","authors":"V. Dimitrov, Ziyang Gao, P. Habegger","doi":"10.4007/annals.2021.194.1.4","DOIUrl":"https://doi.org/10.4007/annals.2021.194.1.4","url":null,"abstract":"Consider a smooth, geometrically irreducible, projective curve of genus $g ge 2$ defined over a number field of degree $d ge 1$. It has at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the number of rational points is bounded only in terms of $g$, $d$, and the Mordell-Weil rank of the curve's Jacobian, thereby answering in the affirmative a question of Mazur. In addition we obtain uniform bounded, in $g$ and $d$, for the number of geometric torsion points of the Jacobian which lie in the image of an Abel-Jacobi map. Both estimates generalize our previous work for $1$-parameter families. Our proof uses Vojta's approach to the Mordell Conjecture, and the key new ingredient is the generalization of a height inequality due to the second- and third-named authors.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49131665","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: 52
Infinitely many Lagrangian fillings 无穷多个拉格朗日填充
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-01-05 DOI: 10.4007/annals.2022.195.1.3
Roger Casals, Honghao Gao
{"title":"Infinitely many Lagrangian fillings","authors":"Roger Casals, Honghao Gao","doi":"10.4007/annals.2022.195.1.3","DOIUrl":"https://doi.org/10.4007/annals.2022.195.1.3","url":null,"abstract":"We prove that all maximal-tb Legendrian torus links (n,m) in the standard contact 3-sphere, except for (2,m),(3,3),(3,4) and (3,5), admit infinitely many Lagrangian fillings in the standard symplectic 4-ball. This is proven by constructing infinite order Lagrangian concordances which induce faithful actions of the modular group PSL(2,Z) and the mapping class group M(0,4) into the coordinate rings of algebraic varieties associated to Legendrian links. Our results imply that there exist Lagrangian concordance monoids with subgroups of exponential-growth, and yield Stein surfaces homotopic to a 2-sphere with infinitely many distinct exact Lagrangian surfaces of higher-genus. We also show that there exist infinitely many satellite and hyperbolic knots with Legendrian representatives admitting infinitely many exact Lagrangian fillings.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47726981","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: 33
Abelian varieties isogenous to no Jacobian 阿贝尔变异同于没有雅可比矩阵
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-01-01 DOI: 10.4007/annals.2020.191.2.7
D. Masser, U. Zannier
{"title":"Abelian varieties isogenous to no Jacobian","authors":"D. Masser, U. Zannier","doi":"10.4007/annals.2020.191.2.7","DOIUrl":"https://doi.org/10.4007/annals.2020.191.2.7","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70185876","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: 7
Index 指数
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-01-01 DOI: 10.4007/annamath.191.3.1031
{"title":"Index","authors":"","doi":"10.4007/annamath.191.3.1031","DOIUrl":"https://doi.org/10.4007/annamath.191.3.1031","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70187325","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
Highly connected 7-manifolds and non-negative sectional curvature 高度连通的7流形和非负截面曲率
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-01-01 DOI: 10.4007/annals.2020.191.3.3
S. Goette, M. Kerin, K. Shankar
{"title":"Highly connected 7-manifolds and non-negative sectional curvature","authors":"S. Goette, M. Kerin, K. Shankar","doi":"10.4007/annals.2020.191.3.3","DOIUrl":"https://doi.org/10.4007/annals.2020.191.3.3","url":null,"abstract":"Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO (3) -invariant metric of non-negative curvature.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186241","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: 26
Index 指数
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2020-01-01 DOI: 10.4007/annamath.192.3.1069
{"title":"Index","authors":"","doi":"10.4007/annamath.192.3.1069","DOIUrl":"https://doi.org/10.4007/annamath.192.3.1069","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70187442","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
Naked singularities for the Einstein vacuum equations: The exterior solution 爱因斯坦真空方程的裸奇点:外部解
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2019-12-18 DOI: 10.4007/annals.2023.198.1.3
I. Rodnianski, Yakov Shlapentokh-Rothman
{"title":"Naked singularities for the Einstein vacuum equations: The exterior solution","authors":"I. Rodnianski, Yakov Shlapentokh-Rothman","doi":"10.4007/annals.2023.198.1.3","DOIUrl":"https://doi.org/10.4007/annals.2023.198.1.3","url":null,"abstract":"In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in $3+1$ dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Connected to this is a new geometric twisting phenomenon which plays the leading role in singularity formation. \u0000Prior to this work, the only known examples of naked singularities were the solutions constructed by Christodoulou for the spherically symmetric Einstein-scalar-field system, as well as other solutions explored numerically for either the spherically symmetric Einstein equations coupled to suitable matter models or for the Einstein equations in higher dimensions.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41711310","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: 8
Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture 尖谱的分离及其在Gan–Gross–Prasad猜想中的应用
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2019-12-16 DOI: 10.4007/annals.2021.194.2.5
Raphael Beuzart-Plessis, Yifeng Liu, Wei Zhang, Xinwen Zhu
{"title":"Isolation of cuspidal spectrum, with application to the\u0000 Gan–Gross–Prasad conjecture","authors":"Raphael Beuzart-Plessis, Yifeng Liu, Wei Zhang, Xinwen Zhu","doi":"10.4007/annals.2021.194.2.5","DOIUrl":"https://doi.org/10.4007/annals.2021.194.2.5","url":null,"abstract":"We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof of the global Gan--Gross--Prasad conjecture and its refinement Ichino--Ikeda conjecture for $mathrm{U}(n)timesmathrm{U}(n+1)$ in the stable case.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43374548","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
Global group laws and equivariant bordism rings 全局群律与等变边界环
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2019-12-16 DOI: 10.4007/annals.2022.195.3.2
M. Hausmann
{"title":"Global group laws and equivariant bordism rings","authors":"M. Hausmann","doi":"10.4007/annals.2022.195.3.2","DOIUrl":"https://doi.org/10.4007/annals.2022.195.3.2","url":null,"abstract":"We prove that the homotopical $A$-equivariant complex bordism ring is isomorphic to the $A$-equivariant Lazard ring for every abelian compact Lie group $A$, settling a conjecture of Greenlees. We also show an analog for homotopical real bordism rings over elementary abelian $2$-groups. This generalizes classical theorems of Quillen on the connection between non-equivariant bordism rings and formal group laws, and extends the case $A=C_2$ due to Hanke--Wiemeler. \u0000We work in the framework of global homotopy theory, which is essential for our proof. Using this framework, we also give an algebraic characterization of the collection of equivariant complex bordism rings as the universal contravariant functor from abelian compact Lie groups to commutative rings that is equipped with a coordinate. More generally, the ring of $n$-fold cooperations of equivariant complex bordism is shown to be universal among such functors equipped with a strict $n$-tuple of coordinates.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43080531","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: 13
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