Journal of the Institute of Mathematics of Jussieu最新文献

{"title":"EXCEPTIONAL SIMPLE REAL LIE ALGEBRAS AND VIA CONTACTIFICATIONS","authors":"Paweł Nurowski","doi":"10.1017/s1474748024000173","DOIUrl":"https://doi.org/10.1017/s1474748024000173","url":null,"abstract":"In Cartan’s PhD thesis, there is a formula defining a certain rank 8 vector distribution in dimension 15, whose algebra of authomorphism is the split real form of the simple exceptional complex Lie algebra <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline3.png\"/> <jats:tex-math> $mathfrak {f}_4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Cartan’s formula is written in the standard Cartesian coordinates in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline4.png\"/> <jats:tex-math> $mathbb {R}^{15}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In the present paper, we explain how to find analogous formulae for the flat models of any bracket generating distribution <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline5.png\"/> <jats:tex-math> $mathcal D$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> whose symbol algebra <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline6.png\"/> <jats:tex-math> $mathfrak {n}({mathcal D})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is constant and 2-step graded, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline7.png\"/> <jats:tex-math> $mathfrak {n}({mathcal D})=mathfrak {n}_{-2}oplus mathfrak {n}_{-1}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. The formula is given in terms of a solution to a certain system of linear algebraic equations determined by two representations <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline8.png\"/> <jats:tex-math> $(rho ,mathfrak {n}_{-1})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline9.png\"/> <jats:tex-math> $(tau ,mathfrak {n}_{-2})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of a Lie algebra <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline10.png\"/> <jats:tex-math> $mathfrak {n}_{00}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> contained in the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000173_inline11.png\"/> <jats:tex-math>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"66 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527979","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":"COHOMOLOGIE DE DE RHAM DU REVÊTEMENT MODÉRÉ DE L’ESPACE DE DRINFELD","authors":"Damien Junger","doi":"10.1017/s1474748024000082","DOIUrl":"https://doi.org/10.1017/s1474748024000082","url":null,"abstract":"Résumé Dans cet article, nous étudions la cohomologie de de Rham du premier revêtement de la tour de Drinfel’d. En particulier, nous obtenons une preuve purement locale du fait que la partie supercuspidale réalise la correspondance de Jacquet-Langlands locale pour <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000082_inline3.png\"/> <jats:tex-math> $mathrm {GL}_n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> en la comparant à la cohomologie rigide de certaines variétés de Deligne-Lusztig. Les représentations obtenues sont analogues à celles qui apparaissent dans la cohomologie <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000082_inline4.png\"/> <jats:tex-math> $ell $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-adique lorsqu’on oublie l’action du groupe de Weil. La preuve repose sur une généralisation d’un résultat d’excision de Grosse-Klönne et de la description explicite du premier revêtement en tant que revêtement cyclique obtenu par l’auteur dans un travail précédent.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"66 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171096","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":"TWISTED GAN–GROSS–PRASAD CONJECTURE FOR CERTAIN TEMPERED L-PACKETS","authors":"Rui Chen, Wee Teck Gan","doi":"10.1017/s1474748024000197","DOIUrl":"https://doi.org/10.1017/s1474748024000197","url":null,"abstract":"In this paper, we investigate the twisted GGP conjecture for certain tempered representations using the theta correspondence and establish some special cases, namely when the L-parameter of the unitary group is the sum of conjugate-dual characters of the appropriate sign.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"45 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151434","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":"WILES DEFECT OF HECKE ALGEBRAS VIA LOCAL-GLOBAL ARGUMENTS","authors":"Gebhard Böckle, Chandrashekhar B. Khare, Jeffrey Manning","doi":"10.1017/s1474748024000021","DOIUrl":"https://doi.org/10.1017/s1474748024000021","url":null,"abstract":"In his work on modularity of elliptic curves and Fermat’s last theorem, A. Wiles introduced two measures of congruences between Galois representations and between modular forms. One measure is related to the order of a Selmer group associated to a newform &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline1.png\"/&gt; &lt;jats:tex-math&gt; $f in S_2(Gamma _0(N))$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; (and closely linked to deformations of the Galois representation &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline2.png\"/&gt; &lt;jats:tex-math&gt; $rho _f$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; associated to &lt;jats:italic&gt;f&lt;/jats:italic&gt;), whilst the other measure is related to the congruence module associated to &lt;jats:italic&gt;f&lt;/jats:italic&gt; (and is closely linked to Hecke rings and congruences between &lt;jats:italic&gt;f&lt;/jats:italic&gt; and other newforms in &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline3.png\"/&gt; &lt;jats:tex-math&gt; $S_2(Gamma _0(N))$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;). The equality of these two measures led to isomorphisms &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline4.png\"/&gt; &lt;jats:tex-math&gt; $R={mathbf T}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; between deformation rings and Hecke rings (via a numerical criterion for isomorphisms that Wiles proved) and showed these rings to be complete intersections. We continue our study begun in [BKM21] of the &lt;jats:italic&gt;Wiles defect&lt;/jats:italic&gt; of deformation rings and Hecke rings (at a newform &lt;jats:italic&gt;f&lt;/jats:italic&gt;) acting on the cohomology of Shimura curves over &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline5.png\"/&gt; &lt;jats:tex-math&gt; ${mathbf Q}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;: It is defined to be the difference between these two measures of congruences. The Wiles defect thus arises from the failure of the Wiles numerical criterion at an augmentation &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000021_inline6.png\"/&gt; &lt;jats:tex-math&gt; $lambda _f:{mathbf T} to {mathcal O}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. In situations we study here, the Taylor–Wiles–Kisin patching method gives an isomorphism &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"24 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140803590","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":"KOBAYASHI-OCHIAI’S FINITENESS THEOREM FOR ORBIFOLD PAIRS OF GENERAL TYPE","authors":"Finn Bartsch, Ariyan Javanpeykar","doi":"10.1017/s1474748024000094","DOIUrl":"https://doi.org/10.1017/s1474748024000094","url":null,"abstract":"Kobayashi–Ochiai proved that the set of dominant maps from a fixed variety to a fixed variety of general type is finite. We prove the natural extension of their finiteness theorem to Campana’s orbifold pairs.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"100 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140608996","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":"ON THE DISTINCTION OF IWAHORI-SPHERICAL DISCRETE SERIES REPRESENTATIONS","authors":"Paul Broussous","doi":"10.1017/s1474748024000185","DOIUrl":"https://doi.org/10.1017/s1474748024000185","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline1.png\" /> <jats:tex-math> $E/F$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a quadratic unramified extension of non-archimedean local fields and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline2.png\" /> <jats:tex-math> $mathbb H$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> a simply connected semisimple algebraic group defined and split over <jats:italic>F</jats:italic>. We establish general results (multiplicities, test vectors) on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline3.png\" /> <jats:tex-math> ${mathbb H} (F)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-distinguished Iwahori-spherical representations of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline4.png\" /> <jats:tex-math> ${mathbb H} (E)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. For discrete series Iwahori-spherical representations of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline5.png\" /> <jats:tex-math> ${mathbb H} (E)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, we prove a numerical criterion of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline6.png\" /> <jats:tex-math> ${mathbb H} (F)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-distinction. As an application, we classify the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline7.png\" /> <jats:tex-math> ${mathbb H} (F)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-distinguished discrete series representations of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline8.png\" /> <jats:tex-math> ${mathbb H} (E)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> corresponding to degree <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748024000185_inline9.png\" /> <jats:tex-math> $1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> characters of the Iwahori-Hecke algebra.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"100 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609156","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":"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":"110 1","pages":""},"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":"23 1","pages":""},"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":"1 1","pages":""},"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":"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":"140 1","pages":""},"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}