{"title":"On endomorphisms of automatic groups","authors":"André Carvalho","doi":"10.1007/s40316-022-00196-8","DOIUrl":"10.1007/s40316-022-00196-8","url":null,"abstract":"<div><p>We extend the definition of the bounded reduction property to endomorphisms of automatic group and find conditions for it to hold. We study endomorphisms with <i>L</i>-quasiconvex image and prove that those with finite kernel satisfy a synchronous version of the bounded reduction property. Finally, we use these techniques to prove <i>L</i>-quasiconvexity of the equalizer of two endomorphisms under certain (strict) conditions.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"21 - 44"},"PeriodicalIF":0.5,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"108895137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Substitution maps in the Robba ring","authors":"Laurent Berger","doi":"10.1007/s40316-022-00195-9","DOIUrl":"10.1007/s40316-022-00195-9","url":null,"abstract":"<div><p>We ask several questions about substitution maps in the Robba ring. These questions are motivated by <i>p</i>-adic Hodge theory and the theory of <i>p</i>-adic dynamical systems. We provide answers to those questions in special cases, thereby generalizing results of Kedlaya, Colmez, and others.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 2","pages":"289 - 302"},"PeriodicalIF":0.5,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49032498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A p-adic Maass–Shimura operator on Mumford curves","authors":"Matteo Longo","doi":"10.1007/s40316-022-00193-x","DOIUrl":"10.1007/s40316-022-00193-x","url":null,"abstract":"<div><p>We study a <i>p</i>-adic Maass–Shimura operator in the context of Mumford curves defined by [15]. We prove that this operator arises from a splitting of the Hodge filtration, thus answering a question in [15]. We also study the relation of this operator with generalized Heegner cycles, in the spirit of [1, 4, 19, 28].</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"139 - 175"},"PeriodicalIF":0.5,"publicationDate":"2022-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-022-00193-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42361957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On abelian (ell )-towers of multigraphs III","authors":"Kevin McGown, Daniel Vallières","doi":"10.1007/s40316-022-00194-w","DOIUrl":"10.1007/s40316-022-00194-w","url":null,"abstract":"<div><p>Let <span>(ell )</span> be a rational prime. Previously, abelian <span>(ell )</span>-towers of multigraphs were introduced which are analogous to <span>(mathbb {Z}_{ell })</span>-extensions of number fields. It was shown that for towers of bouquets, the growth of the <span>(ell )</span>-part of the number of spanning trees behaves in a predictable manner (analogous to a well-known theorem of Iwasawa for <span>(mathbb {Z}_{ell })</span>-extensions of number fields). In this paper, we extend this result to abelian <span>(ell )</span>-towers over an arbitrary connected multigraph (not necessarily simple and not necessarily regular). In order to carry this out, we employ integer-valued polynomials to construct power series with coefficients in <span>(mathbb {Z}_ell )</span> arising from cyclotomic number fields, different than the power series appearing in the prequel. This allows us to study the special value at <span>(u=1)</span> of the Artin–Ihara <i>L</i>-function, when the base multigraph is not necessarily a bouquet.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"1 - 19"},"PeriodicalIF":0.5,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45347802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extended graph 4-manifolds, and Einstein metrics","authors":"Luca F. Di Cerbo","doi":"10.1007/s40316-021-00192-4","DOIUrl":"10.1007/s40316-021-00192-4","url":null,"abstract":"<div><p>We show that extended graph 4-manifolds (as defined by Frigerio–Lafont–Sisto in [12]) do not support Einstein metrics.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"48 1","pages":"269 - 276"},"PeriodicalIF":0.5,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44498126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction : Les schémas de subdivision de Besicovitch et de Cantor","authors":"Serge Dubuc","doi":"10.1007/s40316-021-00190-6","DOIUrl":"10.1007/s40316-021-00190-6","url":null,"abstract":"","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"495 - 498"},"PeriodicalIF":0.5,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50507654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Plus/minus p-adic L-functions for (mathrm {GL}_{2n})","authors":"Rob Rockwood","doi":"10.1007/s40316-021-00191-5","DOIUrl":"10.1007/s40316-021-00191-5","url":null,"abstract":"<div><p>We generalise Pollack’s construction of plus/minus L-functions to certain cuspidal automorphic representations of <span>(mathrm {GL_{2n}})</span> using the <i>p</i>-adic <i>L</i>-functions constructed in work of Barrera Salazar et al. (On <i>p</i>-adic <i>l</i>-functions for <span>(text {GL}_{2n})</span> in finite slope shalika families, 2021). We use these to prove that the complex <i>L</i>-functions of such representations vanish at at most finitely many twists by characters of <i>p</i>-power conductor.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"177 - 193"},"PeriodicalIF":0.5,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-021-00191-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50493153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Various formulations and approximations of incompressible fluid motions in porous media","authors":"Yann Brenier","doi":"10.1007/s40316-021-00178-2","DOIUrl":"10.1007/s40316-021-00178-2","url":null,"abstract":"<div><p>We first recall various formulations and approximations for the motion of an incompressible fluid, in the well-known setting of the Euler equations. Then, we address incompressible motions in porous media, through the Muskat system, which is a friction dominated first order analog of the Euler equations for inhomogeneous incompressible fluids subject to an external potential.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"195 - 206"},"PeriodicalIF":0.5,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45249371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Special issue in honour of Alexander Shnirelman’s 75th birthday","authors":"Dmitry Jakobson, Boris Khesin, Iosif Polterovich","doi":"10.1007/s40316-021-00189-z","DOIUrl":"10.1007/s40316-021-00189-z","url":null,"abstract":"","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"1 - 2"},"PeriodicalIF":0.5,"publicationDate":"2022-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50465479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"P-adic L-functions in universal deformation families","authors":"David Loeffler","doi":"10.1007/s40316-021-00187-1","DOIUrl":"10.1007/s40316-021-00187-1","url":null,"abstract":"<div><p>We construct examples of <i>p</i>-adic <i>L</i>-functions over universal deformation spaces for <span>({{,mathrm{GL},}}_2)</span>. We formulate a conjecture predicting that the natural parameter spaces for <i>p</i>-adic <i>L</i>-functions and Euler systems are not the usual eigenvarieties (parametrising nearly-ordinary families of automorphic representations), but other, larger spaces depending on a choice of a parabolic subgroup, which we call ‘big parabolic eigenvarieties’.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 1","pages":"117 - 137"},"PeriodicalIF":0.5,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-021-00187-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41686659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}