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Motivic invariants of birational maps | Annals of Mathematics 双向映射的动机不变式 | 数学年鉴
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2023-12-29 DOI: 10.4007/annals.2024.199.1.6
Hsueh-Yung Lin, Evgeny Shinder
{"title":"Motivic invariants of birational maps | Annals of Mathematics","authors":"Hsueh-Yung Lin, Evgeny Shinder","doi":"10.4007/annals.2024.199.1.6","DOIUrl":"https://doi.org/10.4007/annals.2024.199.1.6","url":null,"abstract":"<p>We construct invariants of birational maps with values in the Kontsevich–Tschinkel group and in the truncated Grothendieck groups of varieties. These invariants are morphisms of groupoids and are well-suited to investigating the structure of the Grothendieck ring and L-equivalence. Building on known constructions of L-equivalence, we prove new unexpected results about Cremona groups.</p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064082","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
Erratum to “Special subvarieties of non-arithmetic ball quotients and Hodge theory” | Annals of Mathematics 非算术球商的特殊子项与霍奇理论》勘误 | 数学年鉴
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2023-12-29 DOI: 10.4007/annals.2024.199.1.8
Gregorio Baldi, Emmanuel Ullmo
{"title":"Erratum to “Special subvarieties of non-arithmetic ball quotients and Hodge theory” | Annals of Mathematics","authors":"Gregorio Baldi, Emmanuel Ullmo","doi":"10.4007/annals.2024.199.1.8","DOIUrl":"https://doi.org/10.4007/annals.2024.199.1.8","url":null,"abstract":"<h3>No abstract available for this article</h3>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064128","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 reverse Minkowski theorem | Annals of Mathematics 反向闵科夫斯基定理 | 数学年鉴
IF 4.9 1区 数学
Annals of Mathematics Pub Date : 2023-12-29 DOI: 10.4007/annals.2024.199.1.1
Oded Regev, Noah Stephens-Davidowitz
{"title":"A reverse Minkowski theorem | Annals of Mathematics","authors":"Oded Regev, Noah Stephens-Davidowitz","doi":"10.4007/annals.2024.199.1.1","DOIUrl":"https://doi.org/10.4007/annals.2024.199.1.1","url":null,"abstract":"<p>We prove a conjecture due to Dadush, showing that if $mathcal{L} subset mathbb{R}^n$ is a lattice such that $mathrm{det}(mathcal{L}’)ge 1$ for all sublattices $mathcal{L}’ subseteq mathcal{L}$, then $sum_{mathbf{y}in mathcal{L}} e^{-pi t^2 |mathbf{y} |^2} le 3/2$, where $t := 10(log n + 2)$. From this we derive bounds on the number of short lattice vectors, which can be viewed as a partial converse to Minkowski’s celebrated first theorem. We also derive a bound on the covering radius.</p>","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":4.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064088","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
Wreath-like products of groups and their von Neumann algebras I: W^∗-superrigidity 群的环状积及其von Neumann代数I: W^ * -超刚性
1区 数学
Annals of Mathematics Pub Date : 2023-11-01 DOI: 10.4007/annals.2023.198.3.6
Ionuţ Chifan, Adrian Ioana, Denis Osin, Bin Sun
{"title":"Wreath-like products of groups and their von Neumann algebras I: W^∗-superrigidity","authors":"Ionuţ Chifan, Adrian Ioana, Denis Osin, Bin Sun","doi":"10.4007/annals.2023.198.3.6","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.6","url":null,"abstract":"We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group $G$ in a natural family of wreath-like products with property (T) is W$^*$-superrigid: the group von Neumann algebra $text{L}(G)$ remembers the isomorphism class of $G$. This allows us to provide the first examples (in fact, $2^{aleph_0}$ pairwise non-isomorphic examples) of W$^*$-superrigid groups with property (T).","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135370613","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
Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations 硬球气体的统计动力学:波动玻尔兹曼方程和大偏差
1区 数学
Annals of Mathematics Pub Date : 2023-11-01 DOI: 10.4007/annals.2023.198.3.3
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella
{"title":"Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations","authors":"Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella","doi":"10.4007/annals.2023.198.3.3","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.3","url":null,"abstract":"We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square root of the average number of particles, converge to a Gaussian process driven by the fluctuating Boltzmann equation, as predicted by Spohn; (2) large deviations are exponentially small in the average number of particles and are characterized, under regularity assumptions, by a large deviation functional as previously obtained by Rezakhanlou for dynamics with stochastic collisions. The results are valid away from thermal equilibrium, but only for short times. Our strategy is based on uniform a priori bounds on the cumulant generating function, characterizing the fine structure of the small correlations.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103069","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: 25
Schur multipliers in Schatten-von Neumann classes schaten -von Neumann类中的Schur乘数
1区 数学
Annals of Mathematics Pub Date : 2023-11-01 DOI: 10.4007/annals.2023.198.3.5
José M. Conde-Alonso, Adrián M. González-Pérez, Javier Parcet, Eduardo Tablate
{"title":"Schur multipliers in Schatten-von Neumann classes","authors":"José M. Conde-Alonso, Adrián M. González-Pérez, Javier Parcet, Eduardo Tablate","doi":"10.4007/annals.2023.198.3.5","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.5","url":null,"abstract":"We establish a rather unexpected and simple criterion for the boundedness of Schur multipliers $S_M$ on Schatten $p$-classes which solves a conjecture proposed by Mikael de la Salle. Given $1lt plt infty$, a simple form of our main result for $mathbf{R}^n times mathbf{R}^n$ matrices reads as follows: $$big| S_M colon S_p to S_p big|_{mathrm{cb}} lesssim frac{p^2}{p-1} sum_{|gamma| le [frac{n}{2}] +1} Big| |x-y|^{|gamma|} Big{ big| partial_x^gamma M(x,y) big| + big| partial_y^gamma M(x,y) big| Big} Big|_infty.$$ In this form, it is a full matrix (nonToeplitz/nontrigonometric) amplification of the Hörmander-Mikhlin multiplier theorem, which admits lower fractional differentiability orders $sigma > frac{n}{2}$ as well. It trivially includes Arazy's conjecture for $S_p$-multipliers and extends it to $alpha$-divided differences. It also leads to new Littlewood-Paley characterizations of $S_p$-norms and strong applications in harmonic analysis for nilpotent and high rank simple Lie group algebras.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135116920","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: 1
Characterizing finitely generated fields by a single field axiom 用单域公理描述有限生成域
1区 数学
Annals of Mathematics Pub Date : 2023-11-01 DOI: 10.4007/annals.2023.198.3.4
Philip Dittmann, Florian Pop
{"title":"Characterizing finitely generated fields by a single field axiom","authors":"Philip Dittmann, Florian Pop","doi":"10.4007/annals.2023.198.3.4","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.4","url":null,"abstract":"We resolve the Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is an explicit first-order sentence which characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018341","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: 1
Universality for lozenge tiling local statistics 菱形平铺局部统计的普适性
1区 数学
Annals of Mathematics Pub Date : 2023-11-01 DOI: 10.4007/annals.2023.198.3.1
Amol Aggarwal
{"title":"Universality for lozenge tiling local statistics","authors":"Amol Aggarwal","doi":"10.4007/annals.2023.198.3.1","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.1","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135370604","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
Regularity of minimal surfaces near quadratic cones 二次锥附近最小曲面的正则性
1区 数学
Annals of Mathematics Pub Date : 2023-11-01 DOI: 10.4007/annals.2023.198.3.2
Nick Edelen, Luca Spolaor
{"title":"Regularity of minimal surfaces near quadratic cones","authors":"Nick Edelen, Luca Spolaor","doi":"10.4007/annals.2023.198.3.2","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.2","url":null,"abstract":"Hardt-Simon proved that every area-minimizing hypercone $mathbf{C}$ having only an isolated singularity fits into a foliation of $mathbb{R}^{n+1}$ by smooth, area-minimizing hypersurfaces asymptotic to $mathbf{C}$. In this paper we prove that if a stationary $n$-varifold $M$ in the unit ball $B_1 subset mathbb{R}^{n+1}$ lies sufficiently close to a minimizing quadratic cone (for example, the Simons' cone $mathbf{C}^{3,3}$), then $mathrm{spt} M cap B_{1/2}$ is a $C^{1,alpha}$ perturbation of either the cone itself, or some leaf of its associated foliation. In particular, we show that singularities modeled on these cones determine the local structure not only of $M$, but of any nearby minimal surface. Our result also implies the Bernstein-type result of Simon-Solomon, which characterizes area-minimizing hypersurfaces asymptotic to a quadratic cone as either the cone itself, or some leaf of the foliation.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018462","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
Retraction: "Quasi-projectivity of moduli spaces of polarized varieties" 缩回:“偏振变体模空间的拟投影性”
1区 数学
Annals of Mathematics Pub Date : 2023-11-01 DOI: 10.4007/annals.2023.198.3.7
Georg Schumacher, Hajime Tsuji
{"title":"Retraction: \"Quasi-projectivity of moduli spaces of polarized varieties\"","authors":"Georg Schumacher, Hajime Tsuji","doi":"10.4007/annals.2023.198.3.7","DOIUrl":"https://doi.org/10.4007/annals.2023.198.3.7","url":null,"abstract":"","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135370605","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
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