We characterize Gromov hyperbolicity of the quasihyperbolic metric space (Omega,k) by geometric properties of the Ahlfors regular length metric measure space (Omega,d,mu). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition.
{"title":"Gromov hyperbolicity and quasihyperbolic geodesics","authors":"P. Koskela, P. Lammi, Vesna Manojlovi'c","doi":"10.24033/ASENS.2231","DOIUrl":"https://doi.org/10.24033/ASENS.2231","url":null,"abstract":"We characterize Gromov hyperbolicity of the quasihyperbolic metric space (Omega,k) by geometric properties of the Ahlfors regular length metric measure space (Omega,d,mu). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"103 1","pages":"975-990"},"PeriodicalIF":1.9,"publicationDate":"2012-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89854235","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}
Let k be a field, G a smooth connected linear algebraic group and X a homogeneous space of G over k, such that the geometric stabilizers are extensions of a smooth group of multiplicative type by a smooth connected characterfree group. If k has characteristic zero and if X^c is a smooth compactification of X over k, we obtain a formula for the algebraic Brauer group of X^c. Several variants are obtained in positive characteristic p, including the finite field case and the global field case, where the formulae describe the prime-to-p part of the algebraic unramified Brauer group of X, without assuming the existence of a smooth compactification of X. Moreover, assuming that stabilizers are connected, then our formulae hold for the prime-to-p part of the whole unramified Brauer group.
{"title":"Complexes de groupes de type multiplicatif et groupe de Brauer non ramifié des espaces homogènes","authors":"M. Borovoi, C. Demarche, D. Harari","doi":"10.24033/ASENS.2198","DOIUrl":"https://doi.org/10.24033/ASENS.2198","url":null,"abstract":"Let k be a field, G a smooth connected linear algebraic group and X a homogeneous space of G over k, such that the geometric stabilizers are extensions of a smooth group of multiplicative type by a smooth connected characterfree group. If k has characteristic zero and if X^c is a smooth compactification of X over k, we obtain a formula for the algebraic Brauer group of X^c. Several variants are obtained in positive characteristic p, including the finite field case and the global field case, where the formulae describe the prime-to-p part of the algebraic unramified Brauer group of X, without assuming the existence of a smooth compactification of X. Moreover, assuming that stabilizers are connected, then our formulae hold for the prime-to-p part of the whole unramified Brauer group.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"97 1","pages":"651-692"},"PeriodicalIF":1.9,"publicationDate":"2012-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77063076","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}
{"title":"Locally analytic vectors of unitary principal series of ${mathrm {GL}}_2({mathbb {Q}}_p)$","authors":"Ruochuan Liu, Bingyong Xie, Yuancao Zhang","doi":"10.24033/ASENS.2163","DOIUrl":"https://doi.org/10.24033/ASENS.2163","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"60 1","pages":"167-190"},"PeriodicalIF":1.9,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84018174","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}
{"title":"Caractères semi-simples de ${mathrm {G}_2}(F)$, $F$ corps local non archimédien","authors":"Laurent Blasco, Corinne Blondel","doi":"10.24033/ASENS.2182","DOIUrl":"https://doi.org/10.24033/ASENS.2182","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"19 1","pages":"985-1025"},"PeriodicalIF":1.9,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87841212","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}
We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.
{"title":"KAM theory for the Hamiltonian derivative wave equation","authors":"Massimiliano Berti, L. Biasco, M. Procesi","doi":"10.24033/ASENS.2190","DOIUrl":"https://doi.org/10.24033/ASENS.2190","url":null,"abstract":"We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"46 1","pages":"301-373"},"PeriodicalIF":1.9,"publicationDate":"2011-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89107844","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}
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
{"title":"Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation","authors":"N. Tzvetkov, N. Visciglia","doi":"10.24033/ASENS.2189","DOIUrl":"https://doi.org/10.24033/ASENS.2189","url":null,"abstract":"Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"3 1","pages":"249-299"},"PeriodicalIF":1.9,"publicationDate":"2011-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88841054","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}
We prove an unconditional (but slightly weakened) version of the main result of (13), which was, starting from dimension 4, conditional to the Lefschetz standard conjecture. Let X be a variety with trivial Chow groups, (i.e. the cycle class map to cohomology is injective on CH(X)Q). We prove that if the cohomology of a general hypersurface Y in X is "parameterized by cycles of dimension c", then the Chow groups CHi(Y )Q are trivial for i ≤ c − 1.
{"title":"The Generalized Hodge and Bloch Conjectures are Equivalent for General Complete Intersections, II","authors":"C. Voisin","doi":"10.24033/ASENS.2193","DOIUrl":"https://doi.org/10.24033/ASENS.2193","url":null,"abstract":"We prove an unconditional (but slightly weakened) version of the main result of (13), which was, starting from dimension 4, conditional to the Lefschetz standard conjecture. Let X be a variety with trivial Chow groups, (i.e. the cycle class map to cohomology is injective on CH(X)Q). We prove that if the cohomology of a general hypersurface Y in X is \"parameterized by cycles of dimension c\", then the Chow groups CHi(Y )Q are trivial for i ≤ c − 1.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"34 1","pages":"449-475"},"PeriodicalIF":1.9,"publicationDate":"2011-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74643254","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}
Thomas Barnet-Lamb, Toby Gee, D. Geraghty, Richard Taylor
We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.
{"title":"Local-global compatibility for $l=p$, II","authors":"Thomas Barnet-Lamb, Toby Gee, D. Geraghty, Richard Taylor","doi":"10.24033/ASENS.2212","DOIUrl":"https://doi.org/10.24033/ASENS.2212","url":null,"abstract":"We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"28 1","pages":"165-179"},"PeriodicalIF":1.9,"publicationDate":"2011-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72741044","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}
We prove that $mathcal{C}^r$ maps with $r>1$ on a compact surface have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. More precisely we give a sharp upper bound on the so-called symbolic extension entropy, which is the infimum of the topological entropies of all the symbolic extensions. This answers positively a conjecture of S.Newhouse and T.Downarowicz in dimension two and improves a previous result of the author cite{burinv}.
{"title":"Symbolic extensions in intermediate smoothness on surfaces","authors":"David Burguet","doi":"10.24033/ASENS.2167","DOIUrl":"https://doi.org/10.24033/ASENS.2167","url":null,"abstract":"We prove that $mathcal{C}^r$ maps with $r>1$ on a compact surface have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. More precisely we give a sharp upper bound on the so-called symbolic extension entropy, which is the infimum of the topological entropies of all the symbolic extensions. This answers positively a conjecture of S.Newhouse and T.Downarowicz in dimension two and improves a previous result of the author cite{burinv}.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"48 1","pages":"337-362"},"PeriodicalIF":1.9,"publicationDate":"2011-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85809584","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}
Nous construisons un complexe de representations localement analytiques de GL 3 (ℚ p ), associe a certaines representations semi-stables de dimension 3 du groupe de Galois absolu de Qp. Nous montrons ensuite que l'on peut retrouver le (ϕ, N)-module filtre de la representation galoisienne en considerant les morphismes, dans la categorie derivee des D(GL 3 (ℚ p ))-modules, de ce complexe dans le complexe de de Rham de l'espace de Drinfel'd de dimension 2. La preuve requiert le calcul de certains espaces de cohomologie localement analytiques de sous-groupes unipotents a coefficients dans des series principales localement analytiques.
分析我们构建一个复杂的非本地的GL(ℚ3页),结合了一些非semi-stables绝对伽罗瓦群的第三维度的Qp。然后我们才能找回的过滤器(N) -moduleϕ代表处galoisienne morphismes于1968年,在“一类的GL(ℚ3 D (w)) -modules这个复杂的建筑群,de Rham Drinfel’d 2个维度的空间。证明需要计算局部分析主序列中具有系数的单能子群的某些局部分析上同调空间。
{"title":"Représentations localement analytiques de $mathrm {GL}_3(mathbb {Q}_{p})$","authors":"Benjamin Schraen","doi":"10.24033/ASENS.2140","DOIUrl":"https://doi.org/10.24033/ASENS.2140","url":null,"abstract":"Nous construisons un complexe de representations localement analytiques de GL 3 (ℚ p ), associe a certaines representations semi-stables de dimension 3 du groupe de Galois absolu de Qp. Nous montrons ensuite que l'on peut retrouver le (ϕ, N)-module filtre de la representation galoisienne en considerant les morphismes, dans la categorie derivee des D(GL 3 (ℚ p ))-modules, de ce complexe dans le complexe de de Rham de l'espace de Drinfel'd de dimension 2. La preuve requiert le calcul de certains espaces de cohomologie localement analytiques de sous-groupes unipotents a coefficients dans des series principales localement analytiques.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"42 1","pages":"43-145"},"PeriodicalIF":1.9,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80774464","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}
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