Publications of the Research Institute for Mathematical Sciences最新文献

{"title":"Inter-universal Teichmüller Theory I: Construction of Hodge Theaters","authors":"S. Mochizuki","doi":"10.4171/PRIMS/57-1-1","DOIUrl":"https://doi.org/10.4171/PRIMS/57-1-1","url":null,"abstract":"The present paper is the first in a series of four papers, the goal of which is to establish an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve — which we refer to as “inter-universal Teichmüller theory” — by applying the theory of semi-graphs of anabelioids, Frobenioids, the étale theta function, and log-shells developed in earlier papers by the author. We begin by fixing what we call “initial Θ-data”, which consists of an elliptic curve EF over a number field F , and a prime number l ≥ 5, as well as some other technical data satisfying certain technical properties. This data determines various hyperbolic orbicurves that are related via finite étale coverings to the once-punctured elliptic curve XF determined by EF . These finite étale coverings admit various symmetry properties arising from the additive and multiplicative structures on the ring Fl = Z/lZ acting on the l-torsion points of the elliptic curve. We then construct “Θ±ellNF-Hodge theaters” associated to the given Θ-data. These Θ±ellNF-Hodge theaters may be thought of as miniature models of conventional scheme theory in which the two underlying combinatorial dimensions of a number field — which may be thought of as corresponding to the additive and multiplicative structures of a ring or, alternatively, to the group of units and value group of a local field associated to the number field — are, in some sense, “dismantled” or “disentangled” from one another. All Θ±ellNF-Hodge theaters are isomorphic to one another, but may also be related to one another by means of a “Θ-link”, which relates certain Frobenioid-theoretic portions of one Θ±ellNF-Hodge theater to another in a fashion that is not compatible with the respective conventional ring/scheme theory structures. In particular, it is a highly nontrivial problem to relate the ring structures on either side of the Θ-link to one another. This will be achieved, up to certain “relatively mild indeterminacies”, in future papers in the series by applying the absolute anabelian geometry developed in earlier papers by the author. The resulting description of an “alien ring structure” [associated, say, to the domain of the Θ-link] in terms of a given ring structure [associated, say, to the codomain of the Θ-link] will be applied in the final paper of the series to obtain results in diophantine geometry. Finally, we discuss certain technical results concerning profinite conjugates of decomposition and inertia groups in the tempered fundamental group of a p-adic hyperbolic curve that will be of use in the development of the theory of the present series of papers, but are also of independent interest.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":"57 1","pages":"3-207"},"PeriodicalIF":1.2,"publicationDate":"2021-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42493132","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":"Versal Unfolding of Irregular Singularities of a Linear Differential Equation on the Riemann Sphere","authors":"T. Oshima","doi":"10.4171/prims/57-3-6","DOIUrl":"https://doi.org/10.4171/prims/57-3-6","url":null,"abstract":"For a linear differential operator P on P1 with unramified irregular singular points we examine a realization of P as a confluence of singularities of a Fuchsian differential operator P̃ having the same index of rigidity as P , which we call an unfolding of P . We conjecture that this is always possible. For example, if P is rigid, this is true and the unfolding helps us to study the equation Pu = 0.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70902043","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":"Combinatorial Belyi Cuspidalization and Arithmetic Subquotients of the Grothendieck–Teichmüller Group","authors":"Shota Tsujimura","doi":"10.4171/prims/56-4-5","DOIUrl":"https://doi.org/10.4171/prims/56-4-5","url":null,"abstract":"In this paper, we develop a certain combinatorial version of the theory of Belyi cuspidalization developed by Mochizuki. Write Q ⊆ C for the subfield of algebraic numbers ∈ C. We then apply this theory of combinatorial Belyi cuspidalization to certain natural closed subgroups of the Grothendieck-Teichmüller group associated to the field of p-adic numbers [where p is a prime number] and to stably ×μ-indivisible subfields of Q, i.e., subfields for which every finite field extension satisfies the property that every nonzero divisible element in the field extension is a root of unity. 2010 Mathematics Subject Classification: Primary 14H30.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/56-4-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46938338","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":"Boundedness of Weak Fano Pairs with Alpha-Invariants and Volumes Bounded Below","authors":"Weichung Chen","doi":"10.4171/prims/56-3-4","DOIUrl":"https://doi.org/10.4171/prims/56-3-4","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45733684","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":"Algebras of Lorch Analytic Mappings Defined on Uniform Algebras","authors":"Guilherme Mauro, L. A. Moraes","doi":"10.4171/prims/56-3-1","DOIUrl":"https://doi.org/10.4171/prims/56-3-1","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":"56 1","pages":"431-443"},"PeriodicalIF":1.2,"publicationDate":"2020-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49149715","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 Commutants of Generators of $q$-Deformed Araki–Woods von Neumann Algebras","authors":"Panchugopal Bikram, Kunal Mukherjee","doi":"10.4171/prims/58-3-1","DOIUrl":"https://doi.org/10.4171/prims/58-3-1","url":null,"abstract":"The generating abelian subalgebras arsing from vectors in the ergodic component of Hiai's construction of the q-deformed Araki-Woods von Neumann algebras are quasi-split.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46789184","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":"Frobenius-Projective Structures on Curves in Positive Characteristic","authors":"Yuichiro Hoshi","doi":"10.4171/prims/56-2-5","DOIUrl":"https://doi.org/10.4171/prims/56-2-5","url":null,"abstract":"— In the present paper, we study Frobenius-projective structures on projective smooth curves in positive characteristic. The notion of Frobenius-projective structures may be regarded as an analogue, in positive characteristic, of the notion of complex projective structures in the classical theory of Riemann surfaces. By means of the notion of Frobeniusprojective structures, we obtain a relationship between a certain rational function, i.e., a pseudo-coordinate, and a certain collection of data which may be regarded as an analogue, in positive characteristic, of the notion of indigenous bundles in the classical theory of Riemann surfaces, i.e., a Frobenius-indigenous structure. As an application of this relationship, we also prove the existence of certain Frobenius-destabilized locally free coherent sheaves of rank two.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":"56 1","pages":"401-430"},"PeriodicalIF":1.2,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/56-2-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42828693","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":"Subadjunction for Quasi-Log Canonical Pairs and Its Applications","authors":"O. Fujino","doi":"10.4171/prims/58-4-1","DOIUrl":"https://doi.org/10.4171/prims/58-4-1","url":null,"abstract":"We establish a kind of subadjunction formula for quasi-log canonical pairs. As an application, we prove that a connected projective quasi-log canonical pair whose quasi-log canonical class is anti-ample is simply connected and rationally chain connected. We also supplement the cone theorem for quasi-log canonical pairs. More precisely, we prove that every negative extremal ray is spanned by a rational curve. Finally, we treat the notion of Mori hyperbolicity for quasi-log canonical pairs.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45830635","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":"Upper Bounds for Roots of $b$-Functions, following Kashiwara and Lichtin","authors":"Bradley Dirks, M. Mustaţă","doi":"10.4171/prims/58-4-2","DOIUrl":"https://doi.org/10.4171/prims/58-4-2","url":null,"abstract":"By building on a method introduced by Kashiwara and refined by Lichtin, we give upper bounds for the roots of certain b-functions associated to a regular function f in terms of a log resolution of singularities. As applications, we recover with more elementary methods a result of Budur and Saito describing the multiplier ideals of f in terms of the V-filtration of f and a result of the second named author with Popa giving a lower bound for the minimal exponent of f in terms of a log resolution.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44996231","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 Central Sequence Algebras of Tensor Product von Neumann Algebras","authors":"Y. Hashiba","doi":"10.4171/prims/58-2-6","DOIUrl":"https://doi.org/10.4171/prims/58-2-6","url":null,"abstract":"We show that when $M,N_{1},N_{2}$ are tracial von Neumann algebras with $M'cap M^{omega}$ abelian, $M'cap(Mbar{otimes}N_{1})^{omega}$ and $M'cap(Mbar{otimes}N_{2})^{omega}$ commute in $(Mbar{otimes}N_{1}bar{otimes}N_{2})^{omega}$. As a consequence, we obtain information on McDuff decompositions of $rm{II}_{1}$ factors of the form $Mbar{otimes}N$, where $M$ is a non-McDuff factor.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42476829","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}