We study free dg-Lie algebroids over arbitrary derived schemes, and compute their universal enveloping and jet algebras. We also introduce derived twisted connections, and relate them with lifts on twisted square zero extensions. This construction allows us to provide new conceptual approaches of existing results concerning the derived deformation theory of subschemes.
{"title":"Derived Intersections and Free dg-Lie Algebroids","authors":"Julien Grivaux","doi":"10.4171/prims/57-3-11","DOIUrl":"https://doi.org/10.4171/prims/57-3-11","url":null,"abstract":"We study free dg-Lie algebroids over arbitrary derived schemes, and compute their universal enveloping and jet algebras. We also introduce derived twisted connections, and relate them with lifts on twisted square zero extensions. This construction allows us to provide new conceptual approaches of existing results concerning the derived deformation theory of subschemes.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48611171","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":"Kähler Forms for Families of Calabi–Yau Manifolds","authors":"Matthias Braun, Youngook Choi, G. Schumacher","doi":"10.4171/prims/56-1-1","DOIUrl":"https://doi.org/10.4171/prims/56-1-1","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/56-1-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46984218","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 Regular Ground States of the Linear Boson Field in Terms of Soft Modes","authors":"A. Rieckers","doi":"10.4171/prims/56-1-6","DOIUrl":"https://doi.org/10.4171/prims/56-1-6","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/56-1-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49645726","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}
For a stable homotopy category [6], M. Hopkins introduced a Picard group (cf. [11], [4]) as a category consisting of isomorphism classes of invertible objects. For the stable homotopy category of Ln-local spectra, M. Hovey and H. Sadofsky [7] showed that the Picard group is actually a group containing the group of integers as a direct summand. We constructed an injection in [8] from the other summand of the Picard group to the direct sum of the Er-terms E r,r−1 r over r ≥ 2 of the Adams-Novikov spectral sequence converging to the homotopy groups of the Ln-localized sphere spectrum. In this paper, we show in a classical way that the injection is a bijection under a condition.
{"title":"A Note on Hopkins' Picard Groups of the Stable Homotopy Categories of $L_n$-Local Spectra","authors":"K. Shimomura","doi":"10.4171/prims/56-1-8","DOIUrl":"https://doi.org/10.4171/prims/56-1-8","url":null,"abstract":"For a stable homotopy category [6], M. Hopkins introduced a Picard group (cf. [11], [4]) as a category consisting of isomorphism classes of invertible objects. For the stable homotopy category of Ln-local spectra, M. Hovey and H. Sadofsky [7] showed that the Picard group is actually a group containing the group of integers as a direct summand. We constructed an injection in [8] from the other summand of the Picard group to the direct sum of the Er-terms E r,r−1 r over r ≥ 2 of the Adams-Novikov spectral sequence converging to the homotopy groups of the Ln-localized sphere spectrum. In this paper, we show in a classical way that the injection is a bijection under a condition.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47612368","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}
Various constructions for quantum groups have been generalized to $imath$-quantum groups. Such generalization is called $imath$-program. In this paper, we fill one of parts in the $imath$-program. Namely, we provide an equivariant K-theory approach to $imath$-quantum groups associated to the Satake diagram in eqref{eq1}, which is the Langlands dual picture of that constructed in cite{BKLW14}, where a geometric realization of the $imath$-quantum group is provided by using perverse sheaves. As an application of the main results, we prove Li's conjecture cite{L18} for the special cases with the satake diagram in eqref{eq1}.
{"title":"Equivariant K-Theory Approach to $imath$-Quantum Groups","authors":"Zhaobing Fan, Haitao Ma, H. Xiao","doi":"10.4171/prims/58-3-6","DOIUrl":"https://doi.org/10.4171/prims/58-3-6","url":null,"abstract":"Various constructions for quantum groups have been generalized to $imath$-quantum groups. Such generalization is called $imath$-program. In this paper, we fill one of parts in the $imath$-program. Namely, we provide an equivariant K-theory approach to $imath$-quantum groups associated to the Satake diagram in eqref{eq1}, which is the Langlands dual picture of that constructed in cite{BKLW14}, where a geometric realization of the $imath$-quantum group is provided by using perverse sheaves. As an application of the main results, we prove Li's conjecture cite{L18} for the special cases with the satake diagram in eqref{eq1}.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47322633","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 Graph-Theoretical Classification for Reflectable Bases","authors":"S. Azam, M. Soltani, M. Tomie, Yōji Yoshii","doi":"10.4171/prims/55-4-2","DOIUrl":"https://doi.org/10.4171/prims/55-4-2","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/55-4-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48620557","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":"Moderate Degeneration of Kähler–Einstein Manifolds with Negative Ricci Curvature","authors":"S. Takayama","doi":"10.4171/prims/55-4-4","DOIUrl":"https://doi.org/10.4171/prims/55-4-4","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45835760","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}
We obtain a "generalized Franchetta conjecture" type of statement for the Hilbert squares of low genus K3 surfaces, and for the Fano varieties of lines on certain cubic fourfolds.
{"title":"The Generalized Franchetta Conjecture for Some Hyperkähler Fourfolds","authors":"R. Laterveer","doi":"10.4171/prims/55-4-8","DOIUrl":"https://doi.org/10.4171/prims/55-4-8","url":null,"abstract":"We obtain a \"generalized Franchetta conjecture\" type of statement for the Hilbert squares of low genus K3 surfaces, and for the Fano varieties of lines on certain cubic fourfolds.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/55-4-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48301316","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":"Superoscillating Sequences and Hyperfunctions","authors":"F. Colombo, A. Yger, I. Sabadini, D. Struppa","doi":"10.4171/prims/55-4-1","DOIUrl":"https://doi.org/10.4171/prims/55-4-1","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/55-4-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46495053","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}
We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the resolvent density. Afterwards, we establish existence and uniqueness of mild solutions to stochastic wave equations provided some Lipschitz and linear growth conditions. We prove H"older continuity in space and time and compute the H"older exponents. Moreover, we are concerned with the phenomenon of weak intermittency.
{"title":"Stochastic Wave Equations Defined by Fractal Laplacians on Cantor-Like Sets","authors":"Tim Ehnes","doi":"10.4171/prims/58-4-3","DOIUrl":"https://doi.org/10.4171/prims/58-4-3","url":null,"abstract":"We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the resolvent density. Afterwards, we establish existence and uniqueness of mild solutions to stochastic wave equations provided some Lipschitz and linear growth conditions. We prove H\"older continuity in space and time and compute the H\"older exponents. Moreover, we are concerned with the phenomenon of weak intermittency.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49325017","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}
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