Glasgow Mathematical Journal最新文献

{"title":"A note on almost Yamabe solitons","authors":"Wagner Oliveira Costa-Filho","doi":"10.1017/s0017089523000411","DOIUrl":"https://doi.org/10.1017/s0017089523000411","url":null,"abstract":"In this paper, we present a sufficient condition for almost Yamabe solitons to have constant scalar curvature. Additionally, under some geometric scenarios, we provide some triviality and rigidity results for these structures.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On -unramified extensions over imaginary quadratic fields","authors":"Kwang-Seob Kim, Joachim König","doi":"10.1017/s001708952300037x","DOIUrl":"https://doi.org/10.1017/s001708952300037x","url":null,"abstract":"<jats:p>Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300037X_inline2.png\" /> <jats:tex-math> $n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be an integer congruent to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300037X_inline3.png\" /> <jats:tex-math> $0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> or <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300037X_inline4.png\" /> <jats:tex-math> $3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> modulo <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300037X_inline5.png\" /> <jats:tex-math> $4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. Under the assumption of the ABC conjecture, we prove that, given any integer <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300037X_inline6.png\" /> <jats:tex-math> $m$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> fulfilling only a certain coprimeness condition, there exist infinitely many imaginary quadratic fields having an everywhere unramified Galois extension of group <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300037X_inline7.png\" /> <jats:tex-math> $A_n times C_m$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. The same result is obtained unconditionally in special cases.</jats:p>","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"8 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A classification of some thick subcategories in locally noetherian Grothendieck categories","authors":"Kaili Wu, Xinchao Ma","doi":"10.1017/s001708952300040x","DOIUrl":"https://doi.org/10.1017/s001708952300040x","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=\"S001708952300040X_inline1.png\" /> <jats:tex-math> $mathcal{A}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a locally noetherian Grothendieck category. We classify all full subcategories of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300040X_inline2.png\" /> <jats:tex-math> $mathcal{A}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> which are thick and closed under taking arbitrary direct sums and injective envelopes by injective spectrum. This result gives a generalization from the commutative noetherian ring to the locally noetherian Grothendieck category.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"82 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A natural pseudometric on homotopy groups of metric spaces","authors":"Jeremy Brazas, Paul Fabel","doi":"10.1017/s0017089523000393","DOIUrl":"https://doi.org/10.1017/s0017089523000393","url":null,"abstract":"Abstract For a path-connected metric space $(X,d)$ , the $n$ -th homotopy group $pi _n(X)$ inherits a natural pseudometric from the $n$ -th iterated loop space with the uniform metric. This pseudometric gives $pi _n(X)$ the structure of a topological group, and when $X$ is compact, the induced pseudometric topology is independent of the metric $d$ . In this paper, we study the properties of this pseudometric and how it relates to previously studied structures on $pi _n(X)$ . Our main result is that the pseudometric topology agrees with the shape topology on $pi _n(X)$ if $X$ is compact and $LC^{n-1}$ or if $X$ is an inverse limit of finite polyhedra with retraction bonding maps.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"10 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tropical invariants for binary quintics and reduction types of Picard curves","authors":"Paul Alexander Helminck, Yassine El Maazouz, Enis Kaya","doi":"10.1017/s0017089523000344","DOIUrl":"https://doi.org/10.1017/s0017089523000344","url":null,"abstract":"Abstract In this paper, we express the reduction types of Picard curves in terms of tropical invariants associated with binary quintics. We also give a general framework for tropical invariants associated with group actions on arbitrary varieties. The problem of finding tropical invariants for binary forms fits in this general framework by mapping the space of binary forms to symmetrized versions of the Deligne–Mumford compactification $overline{M}_{0,n}$ .","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Notes on hyperelliptic mapping class groups","authors":"Marco Boggi","doi":"10.1017/s0017089523000381","DOIUrl":"https://doi.org/10.1017/s0017089523000381","url":null,"abstract":"Abstract Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural epimorphisms between mapping class groups of surfaces with marked points. We study these groups in a systematic way. An application of this theory is a counterexample to the genus $2$ case of a conjecture by Putman and Wieland on virtual linear representations of mapping class groups. In the last section, we study profinite completions of hyperelliptic mapping class groups: we extend the congruence subgroup property to the general class of hyperelliptic mapping class groups introduced above and then determine the centralizers of multitwists and of open subgroups in their profinite completions.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"66 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the reducing projective dimension over local rings","authors":"Olgur Celikbas, Souvik Dey, Toshinori Kobayashi, Hiroki Matsui","doi":"10.1017/s0017089523000368","DOIUrl":"https://doi.org/10.1017/s0017089523000368","url":null,"abstract":"Abstract In this paper, we are concerned with certain invariants of modules, called reducing invariants, which have been recently introduced and studied by Araya–Celikbas and Araya–Takahashi. We raise the question whether the residue field of each commutative Noetherian local ring has finite reducing projective dimension and obtain an affirmative answer for the question for a large class of local rings. Furthermore, we construct new examples of modules of infinite projective dimension that have finite reducing projective dimension and study several fundamental properties of reducing dimensions, especially properties under local homomorphisms of local rings.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Autocorrelations of characteristic polynomials for the Alternative Circular Unitary Ensemble","authors":"Brad Rodgers, Harshith Sai Vallabhaneni","doi":"10.1017/s0017089523000332","DOIUrl":"https://doi.org/10.1017/s0017089523000332","url":null,"abstract":"Abstract We find closed formulas for arbitrarily high mixed moments of characteristic polynomials of the Alternative Circular Unitary Ensemble, as well as closed formulas for the averages of ratios of characteristic polynomials in this ensemble. A comparison is made to analogous results for the Circular Unitary Ensemble. Both moments and ratios are studied via symmetric function theory and a general formula of Borodin-Olshanski-Strahov.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"25 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Representatives of similarity classes of matrices over PIDs corresponding to ideal classes","authors":"Lucy Knight, Alexander Stasinski","doi":"10.1017/s0017089523000356","DOIUrl":"https://doi.org/10.1017/s0017089523000356","url":null,"abstract":"Abstract For a principal ideal domain $A$ , the Latimer–MacDuffee correspondence sets up a bijection between the similarity classes of matrices in $textrm{M}_{n}(A)$ with irreducible characteristic polynomial $f(x)$ and the ideal classes of the order $A[x]/(f(x))$ . We prove that when $A[x]/(f(x))$ is maximal (i.e. integrally closed, i.e. a Dedekind domain), then every similarity class contains a representative that is, in a sense, close to being a companion matrix. The first step in the proof is to show that any similarity class corresponding to an ideal (not necessarily prime) of degree one contains a representative of the desired form. The second step is a previously unpublished result due to Lenstra that implies that when $A[x]/(f(x))$ is maximal, every ideal class contains an ideal of degree one.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"253 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Helfrich functional for compact surfaces in","authors":"Zhongwei Yao","doi":"10.1017/s0017089523000320","DOIUrl":"https://doi.org/10.1017/s0017089523000320","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline2.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$f;:; Mrightarrow mathbb{C}P^{2}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; be an isometric immersion of a compact surface in the complex projective plane &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline3.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathbb{C}P^{2}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. In this paper, we consider the Helfrich-type functional &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline4.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathcal{H}_{lambda _{1},lambda _{2}}(f)=int _{M}(|H|^{2}+lambda _{1}+lambda _{2} C^{2})textrm{d} M$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, where &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline5.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$lambda _{1}, lambda _{2}in mathbb{R}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; with &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline6.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$lambda _{1}geqslant 0$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline7.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$H$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; and &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline8.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$C$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; are respectively the mean curvature vector and the Kähler function of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline9.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$M$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; in &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231003124134699-0703:S0017089523000320:S0017089523000320_inline10.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathbb{C}P^{2}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. The critic","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"88 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138532318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}