we show that the non CM part of `-adic étale cohomology of any compact quaternionic Shimura variety with coefficients in any automorphic local system is a semisimple Galois representation. If the local system has weight k = (k1, . . . , kd) with all ki of the same parity, the full `-adic étale cohomology is semisimple. For Hilbert modular varieties, analogous results are proved for `-adic intersection cohomology of the Baily-Borel compactification. The proof combines a representation-theoretical criterion of semisimplicity with Eichler-Shimura relations for partial Frobenius morphisms. Résumé : on montre que l’action galoisienne sur la partie sans multiplication complexe de la cohomologie étale d’un faisceau `-adique lisse automorphe sur une variété de Shimura quaternionique compacte est semisimple. Si le poids du faisceau s’écrit k = (k1, . . . , kd), où les ki ont la même parité, toute la cohomologie étale est semi-simple. Les mêmes résultats sont montrés pour la cohomologie d’intersection `-adique de la compactification de Baily-Borel des variétés modulaires de Hilbert. La preuve utilise un critère abstrait de semi-simplicité et les relations d’Eichler-Shimura pour les morphismes de Frobenius partiels.
{"title":"Eichler-Shimura relations and semisimplicity of étale cohomology of quaternionic Shimura varieties","authors":"J. Nekovář","doi":"10.24033/ASENS.2374","DOIUrl":"https://doi.org/10.24033/ASENS.2374","url":null,"abstract":"we show that the non CM part of `-adic étale cohomology of any compact quaternionic Shimura variety with coefficients in any automorphic local system is a semisimple Galois representation. If the local system has weight k = (k1, . . . , kd) with all ki of the same parity, the full `-adic étale cohomology is semisimple. For Hilbert modular varieties, analogous results are proved for `-adic intersection cohomology of the Baily-Borel compactification. The proof combines a representation-theoretical criterion of semisimplicity with Eichler-Shimura relations for partial Frobenius morphisms. Résumé : on montre que l’action galoisienne sur la partie sans multiplication complexe de la cohomologie étale d’un faisceau `-adique lisse automorphe sur une variété de Shimura quaternionique compacte est semisimple. Si le poids du faisceau s’écrit k = (k1, . . . , kd), où les ki ont la même parité, toute la cohomologie étale est semi-simple. Les mêmes résultats sont montrés pour la cohomologie d’intersection `-adique de la compactification de Baily-Borel des variétés modulaires de Hilbert. La preuve utilise un critère abstrait de semi-simplicité et les relations d’Eichler-Shimura pour les morphismes de Frobenius partiels.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"8 1","pages":"1179-1252"},"PeriodicalIF":1.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74503384","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":"Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities","authors":"Yuri Lima, C. Matheus","doi":"10.24033/ASENS.2350","DOIUrl":"https://doi.org/10.24033/ASENS.2350","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"69 1","pages":"1-38"},"PeriodicalIF":1.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86124553","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":"Groups with no parametric Galois realizations","authors":"P. Dèbes","doi":"10.24033/ASENS.2353","DOIUrl":"https://doi.org/10.24033/ASENS.2353","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"89 1","pages":"143-179"},"PeriodicalIF":1.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76265436","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":"le halo spectral","authors":"Fabrizio Andreatta, A. Iovita, V. Pilloni","doi":"10.24033/ASENS.2362","DOIUrl":"https://doi.org/10.24033/ASENS.2362","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"17 1","pages":"603-655"},"PeriodicalIF":1.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90760284","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}
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Actions affines isométriques propres des groupes hyperboliques sur des quotients d’espaces lp Aurélien Alvarez, Vincent Lafforgue
它是一个多学科的开放获取档案，用于科学研究文件的存储和传播，无论它们是否出版。这些文件可能来自法国或国外的教学和研究机构，也可能来自公共或私人研究中心。HAL开放多学科档案旨在存放和传播来自法国或外国教育和研究机构、公共或私人实验室的已发表或未发表的研究级科学文件。双曲群在lp空间商上的等距仿射作用aurelien Alvarez, Vincent Lafforgue
{"title":"Actions affines isométriques propres des groupes hyperboliques sur des quotients d’espaces ℓp","authors":"Aur'elien Alvarez, V. Lafforgue","doi":"10.24033/ASENS.2377","DOIUrl":"https://doi.org/10.24033/ASENS.2377","url":null,"abstract":"HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Actions affines isométriques propres des groupes hyperboliques sur des quotients d’espaces lp Aurélien Alvarez, Vincent Lafforgue","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"67 1","pages":"1389-1398"},"PeriodicalIF":1.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84045937","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":"Geometric quantization and asymptotics of pairings in TQFT","authors":"Renaud Detcherry","doi":"10.24033/ASENS.2382","DOIUrl":"https://doi.org/10.24033/ASENS.2382","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"10 1","pages":"1599-1631"},"PeriodicalIF":1.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73608957","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":"Strongly interacting blow up bubbles for the mass critical nonlinear Schrödinger equation","authors":"Y. Martel, P. Raphaël","doi":"10.24033/ASENS.2364","DOIUrl":"https://doi.org/10.24033/ASENS.2364","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"9 1","pages":"701-737"},"PeriodicalIF":1.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85499423","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 of characteristic zero, R D k[[t]] the ring of formal power series and K D k((t)) its fraction field. Let X be a finite type R-scheme with smooth generic fiber. Let H be the t-adic completion of X and Hη the generic fiber of H. Let Z ⊂ Xσ bea locally closed subset of the special fiber of X. In this article, we establish a relation between the rigid motive of [Z] (the tube of Z in Hη) and the restriction to Z of the nearby motivic sheaf associated with the R-scheme X. Our main result, Theorem 7.1, can be interpreted as a motivic analog of a theorem of Berkovich. As an application, given a rational point x ∈ Xσ, we obtain an equality, in a suitable Grothendieck ring of motives, between the motivic Milnor fiber of Denef-Loeser at x and the class of the rigid motive of the analytic Milnor fiber of Nicaise-Sebag at x.
设k为特征为零的域，R D k[[t]]为形式幂级数环，k D k((t))为其分数域。设X为具有光滑一般纤维的有限型r格式。设H是X的t进补全，Hη是H的一般纤维。设Z∧Xσ是X的特殊纤维的局部闭子集。本文建立了[Z]的刚性动机(Hη中Z的管)与与r -格式X相关的附近动机束对Z的限制之间的关系。我们的主要结果定理7.1可以解释为Berkovich定理的一个动机类比。作为应用，给定一个有理点x∈Xσ，在合适的Grothendieck动机环上，我们得到了Denef-Loeser的动机Milnor纤维在x处与Nicaise-Sebag的解析Milnor纤维在x处的刚性动机类之间的等式。
{"title":"Motives of rigid analytic tubes and nearby motivic sheaves","authors":"J. Ayoub, F. Ivorra, J. Sebag","doi":"10.24033/ASENS.2347","DOIUrl":"https://doi.org/10.24033/ASENS.2347","url":null,"abstract":"Let k be a field of characteristic zero, R D k[[t]] the ring of formal power series and K D k((t)) its fraction field. Let X be a finite type R-scheme with smooth generic fiber. Let H be the t-adic completion of X and Hη the generic fiber of H. Let Z ⊂ Xσ bea locally closed subset of the special fiber of X. In this article, we establish a relation between the rigid motive of [Z] (the tube of Z in Hη) and the restriction to Z of the nearby motivic sheaf associated with the R-scheme X. Our main result, Theorem 7.1, can be interpreted as a motivic analog of a theorem of Berkovich. As an application, given a rational point x ∈ Xσ, we obtain an equality, in a suitable Grothendieck ring of motives, between the motivic Milnor fiber of Denef-Loeser at x and the class of the rigid motive of the analytic Milnor fiber of Nicaise-Sebag at x.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"102 1","pages":"1335-1382"},"PeriodicalIF":1.9,"publicationDate":"2017-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79943918","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}
Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a compact metric space which is a half-dimensional special Kahler manifold outside a singular set of real Hausdorff codimension 2 and is homeomorphic to the base projective space.
{"title":"Collapsing hyperkähler manifolds","authors":"Valentino Tosatti, Yuguang Zhang","doi":"10.24033/ASENS.2433","DOIUrl":"https://doi.org/10.24033/ASENS.2433","url":null,"abstract":"Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a compact metric space which is a half-dimensional special Kahler manifold outside a singular set of real Hausdorff codimension 2 and is homeomorphic to the base projective space.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"22 1","pages":"751-786"},"PeriodicalIF":1.9,"publicationDate":"2017-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73057814","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 show that $mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees and alpha-invariants bounded from below form a bounded family. As a corollary, K-semistable $mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees bounded from below form a bounded family.
{"title":"Boundedness of Q-Fano varieties with degrees and alpha-invariants bounded from below","authors":"Chen Jiang","doi":"10.24033/ASENS.2445","DOIUrl":"https://doi.org/10.24033/ASENS.2445","url":null,"abstract":"We show that $mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees and alpha-invariants bounded from below form a bounded family. As a corollary, K-semistable $mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees bounded from below form a bounded family.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"40 1","pages":"1235-1248"},"PeriodicalIF":1.9,"publicationDate":"2017-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89506962","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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