{"title":"NMJ volume 247 Cover and Front matter","authors":"","doi":"10.1017/nmj.2022.25","DOIUrl":"https://doi.org/10.1017/nmj.2022.25","url":null,"abstract":"","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49331445","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}
C'edric Dion, Antonio Lei, Anwesh Ray, Daniel Vallières
Let $ell $ be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian $ell $ -towers of multigraphs. In this context, growth patterns are realized by certain analogs of Iwasawa invariants, which depend on the prime $ell $ and the abelian $ell $ -tower of multigraphs. We formulate and study statistical questions about the behavior of the Iwasawa $mu $ and $lambda $ invariants.
{"title":"ON THE DISTRIBUTION OF IWASAWA INVARIANTS ASSOCIATED TO MULTIGRAPHS","authors":"C'edric Dion, Antonio Lei, Anwesh Ray, Daniel Vallières","doi":"10.1017/nmj.2023.18","DOIUrl":"https://doi.org/10.1017/nmj.2023.18","url":null,"abstract":"\u0000\t <jats:p>Let <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline1.png\" />\u0000\t\t<jats:tex-math>\u0000$ell $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> be a prime number. The Iwasawa theory of multigraphs is the systematic study of growth patterns in the number of spanning trees in abelian <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline2.png\" />\u0000\t\t<jats:tex-math>\u0000$ell $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>-towers of multigraphs. In this context, growth patterns are realized by certain analogs of Iwasawa invariants, which depend on the prime <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline3.png\" />\u0000\t\t<jats:tex-math>\u0000$ell $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> and the abelian <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline4.png\" />\u0000\t\t<jats:tex-math>\u0000$ell $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula>-tower of multigraphs. We formulate and study statistical questions about the behavior of the Iwasawa <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline5.png\" />\u0000\t\t<jats:tex-math>\u0000$mu $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> and <jats:inline-formula>\u0000\t <jats:alternatives>\u0000\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763023000181_inline6.png\" />\u0000\t\t<jats:tex-math>\u0000$lambda $\u0000</jats:tex-math>\u0000\t </jats:alternatives>\u0000\t </jats:inline-formula> invariants.</jats:p>","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45398484","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}
Abstract Utilizing ultraproducts, Schoutens constructed a big Cohen–Macaulay (BCM) algebra $mathcal {B}(R)$ over a local domain R essentially of finite type over $mathbb {C}$ . We show that if R is normal and $Delta $ is an effective $mathbb {Q}$ -Weil divisor on $operatorname {Spec} R$ such that $K_R+Delta $ is $mathbb {Q}$ -Cartier, then the BCM test ideal $tau _{widehat {mathcal {B}(R)}}(widehat {R},widehat {Delta })$ of $(widehat {R},widehat {Delta })$ with respect to $widehat {mathcal {B}(R)}$ coincides with the multiplier ideal $mathcal {J}(widehat {R},widehat {Delta })$ of $(widehat {R},widehat {Delta })$ , where $widehat {R}$ and $widehat {mathcal {B}(R)}$ are the $mathfrak {m}$ -adic completions of R and $mathcal {B}(R)$ , respectively, and $widehat {Delta }$ is the flat pullback of $Delta $ by the canonical morphism $operatorname {Spec} widehat {R}to operatorname {Spec} R$ . As an application, we obtain a result on the behavior of multiplier ideals under pure ring extensions.
{"title":"BIG COHEN–MACAULAY TEST IDEALS IN EQUAL CHARACTERISTIC ZERO VIA ULTRAPRODUCTS","authors":"T. Yamaguchi","doi":"10.1017/nmj.2022.41","DOIUrl":"https://doi.org/10.1017/nmj.2022.41","url":null,"abstract":"Abstract Utilizing ultraproducts, Schoutens constructed a big Cohen–Macaulay (BCM) algebra \u0000$mathcal {B}(R)$\u0000 over a local domain R essentially of finite type over \u0000$mathbb {C}$\u0000 . We show that if R is normal and \u0000$Delta $\u0000 is an effective \u0000$mathbb {Q}$\u0000 -Weil divisor on \u0000$operatorname {Spec} R$\u0000 such that \u0000$K_R+Delta $\u0000 is \u0000$mathbb {Q}$\u0000 -Cartier, then the BCM test ideal \u0000$tau _{widehat {mathcal {B}(R)}}(widehat {R},widehat {Delta })$\u0000 of \u0000$(widehat {R},widehat {Delta })$\u0000 with respect to \u0000$widehat {mathcal {B}(R)}$\u0000 coincides with the multiplier ideal \u0000$mathcal {J}(widehat {R},widehat {Delta })$\u0000 of \u0000$(widehat {R},widehat {Delta })$\u0000 , where \u0000$widehat {R}$\u0000 and \u0000$widehat {mathcal {B}(R)}$\u0000 are the \u0000$mathfrak {m}$\u0000 -adic completions of R and \u0000$mathcal {B}(R)$\u0000 , respectively, and \u0000$widehat {Delta }$\u0000 is the flat pullback of \u0000$Delta $\u0000 by the canonical morphism \u0000$operatorname {Spec} widehat {R}to operatorname {Spec} R$\u0000 . As an application, we obtain a result on the behavior of multiplier ideals under pure ring extensions.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44361830","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}
Abstract In this note, we prove the semiampleness conjecture for Kawamata log terminal Calabi–Yau (CY) surface pairs over an excellent base ring. As applications, we deduce that generalized abundance and Serrano’s conjecture hold for surfaces. Finally, we study the semiampleness conjecture for CY threefolds over a mixed characteristic DVR.
{"title":"SEMIAMPLENESS FOR CALABI–YAU SURFACES IN POSITIVE AND MIXED CHARACTERISTIC","authors":"F. Bernasconi, L. Stigant","doi":"10.1017/nmj.2022.32","DOIUrl":"https://doi.org/10.1017/nmj.2022.32","url":null,"abstract":"Abstract In this note, we prove the semiampleness conjecture for Kawamata log terminal Calabi–Yau (CY) surface pairs over an excellent base ring. As applications, we deduce that generalized abundance and Serrano’s conjecture hold for surfaces. Finally, we study the semiampleness conjecture for CY threefolds over a mixed characteristic DVR.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48103663","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":"K-STABLE DIVISORS IN \u0000$mathbb {P}^1times mathbb {P}^1times mathbb {P}^2$\u0000 OF DEGREE \u0000$(1,1,2)$","authors":"I. Cheltsov, Kento Fujita, Takashi Kishimoto, Takuzo Okada","doi":"10.1017/nmj.2023.5","DOIUrl":"https://doi.org/10.1017/nmj.2023.5","url":null,"abstract":"Abstract We prove that every smooth divisor in \u0000$mathbb {P}^1times mathbb {P}^1times mathbb {P}^2$\u0000 of degree \u0000$(1,1,2)$\u0000 is K-stable.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48899038","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}
Abstract The aim of this paper is to establish the boundedness of fractional type Marcinkiewicz integral $mathcal {M}_{iota ,rho ,m}$ and its commutator $mathcal {M}_{iota ,rho ,m,b}$ on generalized Morrey spaces and on Morrey spaces over nonhomogeneous metric measure spaces which satisfy the upper doubling and geometrically doubling conditions. Under the assumption that the dominating function $lambda $ satisfies $epsilon $ -weak reverse doubling condition, the author proves that $mathcal {M}_{iota ,rho ,m}$ is bounded on generalized Morrey space $L^{p,phi }(mu )$ and on Morrey space $M^{p}_{q}(mu )$ . Furthermore, the boundedness of the commutator $mathcal {M}_{iota ,rho ,m,b}$ generated by $mathcal {M}_{iota ,rho ,m}$ and regularized $mathrm {BMO}$ space with discrete coefficient (= $widetilde {mathrm {RBMO}}(mu )$ ) on space $L^{p,phi }(mu )$ and on space $M^{p}_{q}(mu )$ is also obtained.
{"title":"FRACTIONAL TYPE MARCINKIEWICZ INTEGRAL AND ITS COMMUTATOR ON NONHOMOGENEOUS SPACES","authors":"G. Lu","doi":"10.1017/nmj.2022.6","DOIUrl":"https://doi.org/10.1017/nmj.2022.6","url":null,"abstract":"Abstract The aim of this paper is to establish the boundedness of fractional type Marcinkiewicz integral \u0000$mathcal {M}_{iota ,rho ,m}$\u0000 and its commutator \u0000$mathcal {M}_{iota ,rho ,m,b}$\u0000 on generalized Morrey spaces and on Morrey spaces over nonhomogeneous metric measure spaces which satisfy the upper doubling and geometrically doubling conditions. Under the assumption that the dominating function \u0000$lambda $\u0000 satisfies \u0000$epsilon $\u0000 -weak reverse doubling condition, the author proves that \u0000$mathcal {M}_{iota ,rho ,m}$\u0000 is bounded on generalized Morrey space \u0000$L^{p,phi }(mu )$\u0000 and on Morrey space \u0000$M^{p}_{q}(mu )$\u0000 . Furthermore, the boundedness of the commutator \u0000$mathcal {M}_{iota ,rho ,m,b}$\u0000 generated by \u0000$mathcal {M}_{iota ,rho ,m}$\u0000 and regularized \u0000$mathrm {BMO}$\u0000 space with discrete coefficient (= \u0000$widetilde {mathrm {RBMO}}(mu )$\u0000 ) on space \u0000$L^{p,phi }(mu )$\u0000 and on space \u0000$M^{p}_{q}(mu )$\u0000 is also obtained.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47020509","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":"NMJ volume 246 Cover and Back matter","authors":"","doi":"10.1017/nmj.2022.10","DOIUrl":"https://doi.org/10.1017/nmj.2022.10","url":null,"abstract":"","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44831459","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 prove that the maximal number of conics in a smooth sextic K3-surface X ⊂ P is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible. §
{"title":"NMJ volume 246 Cover and Front matter","authors":"S. Rao, Quanting Zhao","doi":"10.1017/nmj.2022.9","DOIUrl":"https://doi.org/10.1017/nmj.2022.9","url":null,"abstract":"We prove that the maximal number of conics in a smooth sextic K3-surface X ⊂ P is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible. §","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41450607","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}
Abstract Iwasawa theory of elliptic curves over noncommutative $GL(2)$ extension has been a fruitful area of research. Over such a noncommutative p-adic Lie extension, there exists a structure theorem providing the structure of the dual Selmer groups for elliptic curves in terms of reflexive ideals in the Iwasawa algebra. The central object of this article is to study Iwasawa theory over the $PGL(2)$ extension and connect it with Iwasawa theory over the $GL(2)$ extension, deriving consequences to the structure theorem when the reflexive ideal is the augmentation ideal of the center. We also show how the dual Selmer group over the $GL(2)$ extension being torsion is related with that of the $PGL(2)$ extension.
{"title":"SELMER GROUPS OF ELLIPTIC CURVES OVER THE \u0000$PGL(2)$\u0000 EXTENSION","authors":"Jishnu Ray, R. Sujatha","doi":"10.1017/nmj.2022.14","DOIUrl":"https://doi.org/10.1017/nmj.2022.14","url":null,"abstract":"Abstract Iwasawa theory of elliptic curves over noncommutative \u0000$GL(2)$\u0000 extension has been a fruitful area of research. Over such a noncommutative p-adic Lie extension, there exists a structure theorem providing the structure of the dual Selmer groups for elliptic curves in terms of reflexive ideals in the Iwasawa algebra. The central object of this article is to study Iwasawa theory over the \u0000$PGL(2)$\u0000 extension and connect it with Iwasawa theory over the \u0000$GL(2)$\u0000 extension, deriving consequences to the structure theorem when the reflexive ideal is the augmentation ideal of the center. We also show how the dual Selmer group over the \u0000$GL(2)$\u0000 extension being torsion is related with that of the \u0000$PGL(2)$\u0000 extension.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42441881","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}
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of $a^3b$ -quadrilaterals with all angles being rational degrees. There are $12$ sporadic and $3$ infinite sequences of quadrilaterals admitting the two-layer earth map tilings together with their modifications, and $3$ sporadic quadrilaterals admitting $4$ exceptional tilings. Among them only three quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings are obtained as a byproduct.
{"title":"TILINGS OF THE SPHERE BY CONGRUENT QUADRILATERALS II: EDGE COMBINATION WITH RATIONAL ANGLES","authors":"Yixi Liao, Erxiao Wang","doi":"10.1017/nmj.2023.20","DOIUrl":"https://doi.org/10.1017/nmj.2023.20","url":null,"abstract":"\u0000 Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of \u0000 \u0000 \u0000 \u0000$a^3b$\u0000\u0000 \u0000 -quadrilaterals with all angles being rational degrees. There are \u0000 \u0000 \u0000 \u0000$12$\u0000\u0000 \u0000 sporadic and \u0000 \u0000 \u0000 \u0000$3$\u0000\u0000 \u0000 infinite sequences of quadrilaterals admitting the two-layer earth map tilings together with their modifications, and \u0000 \u0000 \u0000 \u0000$3$\u0000\u0000 \u0000 sporadic quadrilaterals admitting \u0000 \u0000 \u0000 \u0000$4$\u0000\u0000 \u0000 exceptional tilings. Among them only three quadrilaterals are convex. New interesting non-edge-to-edge triangular tilings are obtained as a byproduct.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43638524","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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