Journal of the Institute of Mathematics of Jussieu最新文献

{"title":"GENERALISED QUADRATIC FORMS OVER TOTALLY REAL NUMBER FIELDS","authors":"Tim Browning, Lillian B. Pierce, Damaris Schindler","doi":"10.1017/s1474748024000161","DOIUrl":"https://doi.org/10.1017/s1474748024000161","url":null,"abstract":"We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A NONCOMMUTATIVE ANALOGUE OF CLAUSEN’S VIEW ON THE IDÈLE CLASS GROUP","authors":"Oliver Braunling, Ruben Henrard, Adam-Christiaan van Roosmalen","doi":"10.1017/s1474748024000100","DOIUrl":"https://doi.org/10.1017/s1474748024000100","url":null,"abstract":"<p>Clausen a prédit que le groupe des classes d’idèles de Chevalley d’un corps de nombres <span>F</span> apparaît comme le premier <span>K</span>-groupe de la catégorie des <span>F</span>-espaces vectoriels localement compacts. Cela s’est avéré vrai, et se généralise même aux groupes <span>K</span> supérieurs dans un sens approprié. Nous remplaçons <span>F</span> par une <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240330095737514-0030:S1474748024000100:S1474748024000100_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {Q}$</span></span></img></span></span>-algèbre semi-simple, et obtenons le groupe des classes d’idèles noncommutatif de Fröhlich de manière analogue, modulo les éléments de norme réduite une. Même dans le cas du corps de nombres, notre preuve est plus simple que celle existante, et repose sur le théorème de localisation pour des sous-catégories percolées. Enfin, en utilisant la théorie des corps de classes, nous interprétons la loi de réciprocité d’Hilbert (ainsi qu’une variante noncommutative) en termes de nos résultats.</p><p>Clausen predicted that Chevalley’s idèle class group of a number field <span>F</span> appears as the first <span>K</span>-group of the category of locally compact <span>F</span>-vector spaces. This has turned out to be true and even generalizes to the higher <span>K</span>-groups in a suitable sense. We replace <span>F</span> by a semisimple <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240330095737514-0030:S1474748024000100:S1474748024000100_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {Q}$</span></span></img></span></span>-algebra and obtain Fröhlich’s noncommutative idèle class group in an analogous fashion, modulo the reduced norm one elements. Even in the number field case, our proof is simpler than the existing one and based on the localization theorem for percolating subcategories. Finally, using class field theory as input, we interpret Hilbert’s reciprocity law (as well as a noncommutative variant) in terms of our results.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DYNAMICAL MCDUFF-TYPE PROPERTIES FOR GROUP ACTIONS ON VON NEUMANN ALGEBRAS","authors":"Gábor Szabó, Lise Wouters","doi":"10.1017/s1474748024000057","DOIUrl":"https://doi.org/10.1017/s1474748024000057","url":null,"abstract":"<p>We consider the notion of strong self-absorption for continuous actions of locally compact groups on the hyperfinite II<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240330095137430-0517:S1474748024000057:S1474748024000057_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$_1$</span></span></img></span></span> factor and characterize when such an action is tensorially absorbed by another given action on any separably acting von Neumann algebra. This extends the well-known McDuff property for von Neumann algebras and is analogous to the core theorems around strongly self-absorbing C<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240330095137430-0517:S1474748024000057:S1474748024000057_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$^*$</span></span></img></span></span>-dynamics. Given a countable discrete group <span>G</span> and an amenable action <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240330095137430-0517:S1474748024000057:S1474748024000057_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$Gcurvearrowright M$</span></span></img></span></span> on any separably acting semifinite von Neumann algebra, we establish a type of measurable local-to-global principle: If a given strongly self-absorbing <span>G</span>-action is suitably absorbed at the level of each fibre in the direct integral decomposition of <span>M</span>, then it is tensorially absorbed by the action on <span>M</span>. As a direct application of Ocneanu’s theorem, we deduce that if <span>M</span> has the McDuff property, then every amenable <span>G</span>-action on <span>M</span> has the equivariant McDuff property, regardless whether <span>M</span> is assumed to be injective or not. By employing Tomita–Takesaki theory, we can extend the latter result to the general case, where <span>M</span> is not assumed to be semifinite.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THE p-ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMES – CORRIGENDUM","authors":"Daniel Disegni","doi":"10.1017/s147474802400001x","DOIUrl":"https://doi.org/10.1017/s147474802400001x","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140755060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THERMODYNAMIC FORMALISM FOR AMENABLE GROUPS AND COUNTABLE STATE SPACES","authors":"Elmer R. Beltrán, Rodrigo Bissacot, Luísa Borsato, Raimundo Briceño","doi":"10.1017/s1474748024000112","DOIUrl":"https://doi.org/10.1017/s1474748024000112","url":null,"abstract":"Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties, such as an infimum rule. Next, we extend the definitions of different notions of Gibbs measures and prove their existence and equivalence, given some regularity and normalization criteria on the potential. Finally, we provide a family of potentials that nontrivially satisfy the conditions for having this equivalence and a nonempty range of inverse temperatures where uniqueness holds.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"AN EFFECTIVE UPPER BOUND FOR ANTI-CANONICAL VOLUMES OF SINGULAR FANO THREEFOLDS","authors":"Chen Jiang, Yu Zou","doi":"10.1017/s1474748024000070","DOIUrl":"https://doi.org/10.1017/s1474748024000070","url":null,"abstract":"<p>For a real number <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$0&lt;epsilon &lt;1/3$</span></span></img></span></span>, we show that the anti-canonical volume of an <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$epsilon $</span></span></img></span></span>-klt Fano <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$3$</span></span></img></span></span>-fold is at most <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$3,200/epsilon ^4$</span></span></img></span></span>, and the order <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$O(1/epsilon ^4)$</span></span></img></span></span> is sharp.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140074722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS","authors":"Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu","doi":"10.1017/s1474748023000397","DOIUrl":"https://doi.org/10.1017/s1474748023000397","url":null,"abstract":"<p>We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between <span>Salié</span> sums and to a new equidistribution estimate for the set of modular roots of primes.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"JMJ volume 23 issue 2 Cover and Back matter","authors":"","doi":"10.1017/s1474748024000136","DOIUrl":"https://doi.org/10.1017/s1474748024000136","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140272708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"JMJ volume 23 issue 2 Cover and Front matter","authors":"","doi":"10.1017/s1474748024000124","DOIUrl":"https://doi.org/10.1017/s1474748024000124","url":null,"abstract":"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140283137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PERFECTING GROUP SCHEMES","authors":"Kevin Coulembier, Geordie Williamson","doi":"10.1017/s1474748024000033","DOIUrl":"https://doi.org/10.1017/s1474748024000033","url":null,"abstract":"We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups and obtains a bijection with the set of classifying spaces of compact connected Lie groups topologically localised away from the characteristic. We also study the representations of perfectly reductive groups. We establish a highest weight classification of simple modules, the decomposition into blocks, and relate extension groups to those of the underlying abstract group.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}