We establish the boundedness of the Erdélyi-Kober fractional integral operators on ball Banach function spaces. In particular, it gives the boundedness of the Erdélyi-Kober fractional integral operators on amalgam spaces and Morrey spaces. Mathematics Subject Classification (2010). Primary: 26A33; Secondary: 46E30.
{"title":"Erdélyi–Kober fractional integral operators on ball Banach function spaces","authors":"K. Ho","doi":"10.4171/RSMUP/72","DOIUrl":"https://doi.org/10.4171/RSMUP/72","url":null,"abstract":"We establish the boundedness of the Erdélyi-Kober fractional integral operators on ball Banach function spaces. In particular, it gives the boundedness of the Erdélyi-Kober fractional integral operators on amalgam spaces and Morrey spaces. Mathematics Subject Classification (2010). Primary: 26A33; Secondary: 46E30.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"18 1","pages":"93-106"},"PeriodicalIF":0.0,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75470790","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":"Hasse–Witt matrices for polynomials, and applications","authors":"Régis Blache","doi":"10.4171/RSMUP/74","DOIUrl":"https://doi.org/10.4171/RSMUP/74","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"103 1","pages":"117-152"},"PeriodicalIF":0.0,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80305799","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":"On the $mathcal{F}^*$-norm of a finite group","authors":"Quanfu Yan, Zhencai Shen","doi":"10.4171/RSMUP/77","DOIUrl":"https://doi.org/10.4171/RSMUP/77","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"126 1","pages":"181-190"},"PeriodicalIF":0.0,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87680183","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}
In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.
本文给出了射影空间中超曲面上完全交环的变分Hodge猜想的一个新的简化证明。
{"title":"Variational Hodge conjecture for complete intersections on hypersurfaces in projective space","authors":"R. Kloosterman","doi":"10.4171/RSMUP/110","DOIUrl":"https://doi.org/10.4171/RSMUP/110","url":null,"abstract":"In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88499899","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}
Given a transitive DG-Lie algebroid $(mathcal{A}, rho)$ over a smooth separated scheme $X$ of finite type over a field $mathbb{K}$ of characteristic $0$ we define a notion of connection $nabla colon mathbf{R}Gamma(X,mathrm{Ker} rho) to mathbf{R}Gamma (X,Omega_X^1[-1]otimes mathrm{Ker} rho)$ and construct an $L_infty$ morphism between DG-Lie algebras $f colon mathbf{R}Gamma(X, mathrm{Ker} rho) rightsquigarrowmathbf{R}Gamma(X, Omega_X^{leq 1} [2])$ associated to a connection and to a cyclic form on the DG-Lie algebroid. In this way, we obtain a lifting of the first component of the modified Buchweitz-Flenner semiregularity map in the algebraic context, which has an application to the deformation theory of coherent sheaves on $X$ admitting a finite locally free resolution. Another application is to the deformations of (Zariski) principal bundles on $X$.
{"title":"Cyclic forms on DG-Lie algebroids and semiregularity","authors":"E. Lepri","doi":"10.4171/rsmup/129","DOIUrl":"https://doi.org/10.4171/rsmup/129","url":null,"abstract":"Given a transitive DG-Lie algebroid $(mathcal{A}, rho)$ over a smooth separated scheme $X$ of finite type over a field $mathbb{K}$ of characteristic $0$ we define a notion of connection $nabla colon mathbf{R}Gamma(X,mathrm{Ker} rho) to mathbf{R}Gamma (X,Omega_X^1[-1]otimes mathrm{Ker} rho)$ and construct an $L_infty$ morphism between DG-Lie algebras $f colon mathbf{R}Gamma(X, mathrm{Ker} rho) rightsquigarrowmathbf{R}Gamma(X, Omega_X^{leq 1} [2])$ associated to a connection and to a cyclic form on the DG-Lie algebroid. In this way, we obtain a lifting of the first component of the modified Buchweitz-Flenner semiregularity map in the algebraic context, which has an application to the deformation theory of coherent sheaves on $X$ admitting a finite locally free resolution. Another application is to the deformations of (Zariski) principal bundles on $X$.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80081496","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}
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties. We provide a construction of the central seminormalization by a decomposition theorem in elementary central gluings. The existence of a central seminormalization is established in the affine case and for real schemes.
{"title":"Central algebraic geometry and seminormality","authors":"J. Monnier","doi":"10.4171/rsmup/124","DOIUrl":"https://doi.org/10.4171/rsmup/124","url":null,"abstract":"We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties. We provide a construction of the central seminormalization by a decomposition theorem in elementary central gluings. The existence of a central seminormalization is established in the affine case and for real schemes.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"127 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89206597","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}
We prove that for any locally finite group there is an extension of the same cardinality which is indecomposable for almost all regular cardinals smaller than its cardinality. Note that a group G is called θ-indecomposable when for every increasing sequence 〈Gi : i < θ〉 of subgroups with union G there is i < θ such that G = Gi. Mathematics Subject Classification (2010). Primary:20A10,03C60
{"title":"Density of indecomposable locally finite groups","authors":"S. Shelah","doi":"10.4171/rsmup/68","DOIUrl":"https://doi.org/10.4171/rsmup/68","url":null,"abstract":"We prove that for any locally finite group there is an extension of the same cardinality which is indecomposable for almost all regular cardinals smaller than its cardinality. Note that a group G is called θ-indecomposable when for every increasing sequence 〈Gi : i < θ〉 of subgroups with union G there is i < θ such that G = Gi. Mathematics Subject Classification (2010). Primary:20A10,03C60","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"69 1","pages":"253-270"},"PeriodicalIF":0.0,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74211412","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}
In cotorsion theories, the cotorsion pairs (SF ,MC) of strongly flat and Matlis-cotorsion modules, and (F , EC) of flat and Enochs-cotorsion modules play important roles. We introduce a new cotorsion pair that in general lies properly between these two (in the partial order generally accepted for cotorsion pairs), and discuss its properties over commutative rings. In particular, we characterize the commutative rings over which this is a perfect cotorsion pair. Our results may shed more light on the relation between the two old cotorsion pairs.
{"title":"On a new cotorsion pair","authors":"L. Fuchs, Sang Bum Lee","doi":"10.4171/rsmup/61","DOIUrl":"https://doi.org/10.4171/rsmup/61","url":null,"abstract":"In cotorsion theories, the cotorsion pairs (SF ,MC) of strongly flat and Matlis-cotorsion modules, and (F , EC) of flat and Enochs-cotorsion modules play important roles. We introduce a new cotorsion pair that in general lies properly between these two (in the partial order generally accepted for cotorsion pairs), and discuss its properties over commutative rings. In particular, we characterize the commutative rings over which this is a perfect cotorsion pair. Our results may shed more light on the relation between the two old cotorsion pairs.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"42 1","pages":"129-143"},"PeriodicalIF":0.0,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74583078","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}
Let $R$ be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate $R$. We restrict to the class of prime divisors that dominate $R$ and show that if a collection of such prime divisors is taken below a certain ``level,'' then the intersection is an almost Dedekind domain having the property that every nonzero ideal can be represented uniquely as an irredundant intersection of powers of maximal ideals.
{"title":"The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two","authors":"B. Olberding, W. Heinzer","doi":"10.4171/rsmup/62","DOIUrl":"https://doi.org/10.4171/rsmup/62","url":null,"abstract":"Let $R$ be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate $R$. We restrict to the class of prime divisors that dominate $R$ and show that if a collection of such prime divisors is taken below a certain ``level,'' then the intersection is an almost Dedekind domain having the property that every nonzero ideal can be represented uniquely as an irredundant intersection of powers of maximal ideals.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73901547","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":"Quasibases for nonseparable $p$-groups","authors":"O. Mutzbauer, E. Toubassi, Andrija Vodopivec","doi":"10.4171/rsmup/65","DOIUrl":"https://doi.org/10.4171/rsmup/65","url":null,"abstract":"","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"63 1","pages":"197-215"},"PeriodicalIF":0.0,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75350322","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}
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