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Annales Scientifiques De L Ecole Normale Superieure最新文献

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On the fields of definition of Hodge loci 霍奇位点的定义领域
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI: 10.24033/asens.2555
Bruno Klingler, Anna Otwinowska, David Urbanik
{"title":"On the fields of definition of Hodge loci","authors":"Bruno Klingler, Anna Otwinowska, David Urbanik","doi":"10.24033/asens.2555","DOIUrl":"https://doi.org/10.24033/asens.2555","url":null,"abstract":"A polarizable variation of Hodge structure over a smooth complex quasi projective variety $S$ is said to be defined over a number field $L$ if $S$ and the algebraic connection associated to the variation are both defined over $L$. Conjecturally any special subvariety (also called an irreducible component of the Hodge locus) for such variations is defined over $overline{mathbb{Q}}$, and its Galois conjugates are also special subvarieties. We prove this conjecture for special subvarieties satisfying a simple monodromy condition. As a corollary we reduce the conjecture that special subvarieties for variation of Hodge structures defined over a number field are defined over $overline{mathbb{Q}}$ to the case of special points.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135647333","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
A dichotomy for minimal hypersurfaces in manifolds thick at infinity 无穷厚流形中最小超曲面的二分法
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI: 10.24033/asens.2550
Antoine SONG
{"title":"A dichotomy for minimal hypersurfaces in manifolds thick at infinity","authors":"Antoine SONG","doi":"10.24033/asens.2550","DOIUrl":"https://doi.org/10.24033/asens.2550","url":null,"abstract":"Let $(M^{n+1},g)$ be a complete $(n+1)$-dimensional Riemannian manifold with $2leq nleq 6$. Our main theorem generalizes the solution of Yau's conjecture for minimal surfaces and builds on a result of Gromov. Suppose that $(M,g)$ is thick at infinity, i.e. any connected finite volume complete minimal hypersurface is closed. Then the following dichotomy holds for the space of closed hypersurfaces in $M$: either there are infinitely many saddle points of the $n$-volume functional, or there is none. \u0000Additionally, we give a new short proof of the existence of a finite volume minimal hypersurface if $(M,g)$ has finite volume, we check Yau's conjecture for finite volume hyperbolic 3-manifolds and we extend the density result of Irie-Marques-Neves when $(M,g)$ is shrinking to zero at infinity.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135739912","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: 17
Applications of forcing theory to homeomorphisms of the closed annulus 强迫理论在闭合环的同胚中的应用
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI: 10.24033/asens.2552
Jonathan Conejeros, Fabio Armando Tal
{"title":"Applications of forcing theory to homeomorphisms of the closed annulus","authors":"Jonathan Conejeros, Fabio Armando Tal","doi":"10.24033/asens.2552","DOIUrl":"https://doi.org/10.24033/asens.2552","url":null,"abstract":"This paper studies homeomorphisms of the closed annulus that are isotopic to the identity from the viewpoint of rotation theory, using a newly developed forcing theory for surface homeomorphisms. Our first result is a solution to the so called strong form of Boyland's Conjecture on the closed annulus: Assume $f$ is a homeomorphism of $overline{mathbb{A}}:=(mathbb{R}/mathbb{Z})times [0,1]$ which is isotopic to the identity and preserves a Borel probability measure $mu$ with full support. We prove that if the rotation set of $f$ is a non-trivial segment, then the rotation number of the measure $mu$ cannot be an endpoint of this segment. We also study the case of homeomorphisms such that $mathbb{A}=(mathbb{R}/mathbb{Z})times (0,1)$ is a region of instability of $f$. We show that, if the rotation numbers of the restriction of $f$ to the boundary components lies in the interior of the rotation set of $f$, then $f$ has uniformly bounded deviations from its rotation set. Finally, by combining this last result and recent work on realization of rotation vectors for annular continua, we obtain that if $f$ is any area-preserving homeomorphism of $overline{mathbb{A}}$ isotopic to the identity, then for every real number $rho$ in the rotation set of $f$, there exists an associated Aubry-Mather set, that is, a compact $f$-invariant set such that every point in this set has a rotation number equal to $rho$. This extends a result by P. Le Calvez previously known only for diffeomorphisms.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135648201","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: 5
Intermediate Jacobians and rationality over arbitrary fields 任意域上的中间雅可比矩阵和合理性
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI: 10.24033/asens.2549
Olivier Benoist, Olivier Wittenberg
{"title":"Intermediate Jacobians and rationality over arbitrary fields","authors":"Olivier Benoist, Olivier Wittenberg","doi":"10.24033/asens.2549","DOIUrl":"https://doi.org/10.24033/asens.2549","url":null,"abstract":"We prove that a three-dimensional smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. To do so, we develop a theory of intermediate Jacobians for geometrically rational threefolds over arbitrary, not necessarily perfect, fields. As a consequence, we obtain the first examples of smooth projective varieties over a field k which have a k-point, and are rational over a purely inseparable field extension of k, but not over k.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135647332","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
Loop equations and a proof of Zvonkine's $qr$-ELSV formula 循环方程和Zvonkine的$qr$-ELSV公式的证明
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI: 10.24033/asens.2553
Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov, Sergey Shadrin
{"title":"Loop equations and a proof of Zvonkine's $qr$-ELSV formula","authors":"Petr Dunin-Barkowski, Reinier Kramer, Alexandr Popolitov, Sergey Shadrin","doi":"10.24033/asens.2553","DOIUrl":"https://doi.org/10.24033/asens.2553","url":null,"abstract":"We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its orbifold generalization, the $qr$-ELSV formula, proposed recently in [KLPS17].","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135647331","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: 16
Reconstructing maps out of groups 从组中重建地图
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI: 10.24033/asens.2551
Kathryn Mann, Maxime Wolff
{"title":"Reconstructing maps out of groups","authors":"Kathryn Mann, Maxime Wolff","doi":"10.24033/asens.2551","DOIUrl":"https://doi.org/10.24033/asens.2551","url":null,"abstract":"We show that, in many situations, a homeomorphism $f$ of a manifold $M$ may be recovered from the (marked) isomorphism class of a finitely generated group of homeomorphisms containing $f$. As an application, we relate the notions of {em critical regularity} and of {em differentiable rigidity}, give examples of groups of diffeomorphisms of 1-manifolds with strong differential rigidity, and in so doing give an independent, short proof of a recent result of Kim and Koberda that there exist finitely generated groups of $C^alpha$ diffeomorphisms of a 1-manifold $M$, not embeddable into $mathrm{Diff}^beta(M)$ for any $beta > alpha > 1$.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135648199","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: 10
Motivic cohomology of quaternionic Shimura varieties and level raising 四元数志村变异的动机上同性及其水平提升
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI: 10.24033/asens.2554
Rong ZHOU
{"title":"Motivic cohomology of quaternionic Shimura varieties and level raising","authors":"Rong ZHOU","doi":"10.24033/asens.2554","DOIUrl":"https://doi.org/10.24033/asens.2554","url":null,"abstract":"We study the motivic cohomology of the special fiber of quaternionic Shimura varieties at a prime of good reduction. We exhibit classes in these motivic cohomology groups and use this to give an explicit geometric realization of level raising between Hilbert modular forms. The main ingredient for our construction is a form of Ihara's Lemma for compact quaternionic Shimura surfaces which we prove by generalizing a method of Diamond-Taylor. Along the way we also verify the Hecke orbit conjecture for these quaternionic Shimura varieties which is a key input for our proof of Ihara's Lemma.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744194","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: 6
Specialization of Néron-Severi groups in positive characteristic nsamron - severi群体专业化的积极特征
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-02 DOI: 10.24033/asens.2542
Emiliano Ambrosi
{"title":"Specialization of Néron-Severi groups in positive characteristic","authors":"Emiliano Ambrosi","doi":"10.24033/asens.2542","DOIUrl":"https://doi.org/10.24033/asens.2542","url":null,"abstract":"Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a reduced scheme $X$, smooth, geometrically connected, separated and of finite type over $k$ and a smooth proper morphism $f:Yrightarrow X$. The main result of this paper is that there are \"lots\" of closed points $xin X$ such that the fibre of $f$ at $x$ has the same geometric Picard rank as the generic fibre. If $X$ is a curve we show that this is true for all but finitely many $k$-rational points. In characteristic zero, these results have been proved by Andre (existence) and Cadoret-Tamagawa (finiteness) using Hodge theoretic methods. To extend the argument in positive characteristic we use the variational Tate conjecture in crystalline cohomology, the comparison between different $p$-adic cohomology theories and independence techniques. The result has applications to the Tate conjecture for divisors, uniform boundedness of Brauer groups, proper families of projective varieties and to the study of families of hyperplane sections of smooth projective varieties.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790104","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: 9
Positroid varieties and cluster algebras 正电子变异体与簇代数
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-02 DOI: 10.24033/asens.2545
Pavel Galashin, Thomas Lam
{"title":"Positroid varieties and cluster algebras","authors":"Pavel Galashin, Thomas Lam","doi":"10.24033/asens.2545","DOIUrl":"https://doi.org/10.24033/asens.2545","url":null,"abstract":"We show that the coordinate ring of an open positroid variety coincides with the cluster algebra associated to a Postnikov diagram. This confirms conjectures of Postnikov, Muller--Speyer, and Leclerc, and generalizes results of Scott and Serhiyenko--Sherman-Bennett--Williams.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790679","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: 29
Large deviations for random walks on Gromov-hyperbolic spaces gromov -双曲空间上随机游走的大偏差
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-02 DOI: 10.24033/asens.2546
Adrien Boulanger, Pierre Mathieu, Cagri Sert, Alessandro Sisto
{"title":"Large deviations for random walks on Gromov-hyperbolic spaces","authors":"Adrien Boulanger, Pierre Mathieu, Cagri Sert, Alessandro Sisto","doi":"10.24033/asens.2546","DOIUrl":"https://doi.org/10.24033/asens.2546","url":null,"abstract":"Let $Gamma$ be a countable group acting on a geodesic Gromov-hyperbolic metric space $X$ and $mu$ a probability measure on $Gamma$ whose support generates a non-elementary subsemigroup. Under the assumption that $mu$ has a finite exponential moment, we establish large deviations results for the distance and the translation length of a random walk with driving measure $mu$. From our results, we deduce a special case of a conjecture regarding large deviations of spectral radii of random matrix products.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790681","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
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