Pub Date : 2022-09-11DOI: 10.2140/pjm.2022.319.259
Van Thinh Dao
{"title":"Average size of 2-Selmer groups of Jacobians of odd hyperelliptic curves over function fields","authors":"Van Thinh Dao","doi":"10.2140/pjm.2022.319.259","DOIUrl":"https://doi.org/10.2140/pjm.2022.319.259","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43367393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-11DOI: 10.2140/pjm.2022.319.439
Lingzhong Zeng, He-Jun Sun
{"title":"Eigenvalues of the drifting Laplacian on smooth metric measure spaces","authors":"Lingzhong Zeng, He-Jun Sun","doi":"10.2140/pjm.2022.319.439","DOIUrl":"https://doi.org/10.2140/pjm.2022.319.439","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42362871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-28DOI: 10.2140/pjm.2022.319.129
Jing Huang, W. Xiao
Let $mathfrak{g}$ be a reductive Lie algebra over $mathbb{C}$. For any simple weight module of $mathfrak{g}$ with finite-dimensional weight spaces, we show that its Dirac cohomology is vanished unless it is a highest weight module. This completes the calculation of Dirac cohomology for simple weight modules since the Dirac cohomology of simple highest weight modules was carried out in our previous work. We also show that the Dirac index pairing of two weight modules which have infinitesimal characters agrees with their Euler-Poincar'{e} pairing. The analogue of this result for Harish-Chandra modules is a consequence of the Kazhdan's orthogonality conjecture which was settled by the first named author and Binyong Sun.
{"title":"Dirac cohomology and orthogonality relations for weight modules","authors":"Jing Huang, W. Xiao","doi":"10.2140/pjm.2022.319.129","DOIUrl":"https://doi.org/10.2140/pjm.2022.319.129","url":null,"abstract":"Let $mathfrak{g}$ be a reductive Lie algebra over $mathbb{C}$. For any simple weight module of $mathfrak{g}$ with finite-dimensional weight spaces, we show that its Dirac cohomology is vanished unless it is a highest weight module. This completes the calculation of Dirac cohomology for simple weight modules since the Dirac cohomology of simple highest weight modules was carried out in our previous work. We also show that the Dirac index pairing of two weight modules which have infinitesimal characters agrees with their Euler-Poincar'{e} pairing. The analogue of this result for Harish-Chandra modules is a consequence of the Kazhdan's orthogonality conjecture which was settled by the first named author and Binyong Sun.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80158719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-13DOI: 10.2140/pjm.2023.322.221
John K. Aceti, Jeremy Brazas
When non-trivial local structures are present in a topological space $X$, a common approach to characterizing the isomorphism type of the $n$-th homotopy group $pi_n(X,x_0)$ is to consider the image of $pi_n(X,x_0)$ in the $n$-th v{C}ech homotopy group $check{pi}_n(X,x_0)$ under the canonical homomorphism $Psi_{n}:pi_n(X,x_0)to check{pi}_n(X,x_0)$. The subgroup $ker(Psi_n)$ is the obstruction to this tactic as it consists of precisely those elements of $pi_n(X,x_0)$, which cannot be detected by polyhedral approximations to $X$. In this paper, we use higher dimensional analogues of Spanier groups to characterize $ker(Psi_n)$. In particular, we prove that if $X$ is paracompact, Hausdorff, and $LC^{n-1}$, then $ker(Psi_n)$ is equal to the $n$-th Spanier group of $X$. We also use the perspective of higher Spanier groups to generalize a theorem of Kozlowski-Segal, which gives conditions ensuring that $Psi_{n}$ is an isomorphism.
当拓扑空间$X$中存在非平凡局部结构时，刻画第$n$-个同伦群$pi_n（X，X_0）$的同构类型的一种常见方法是考虑第$n$个同伦组$pi_n（X，X_0）${C}ech正则同态$Psi_｛n｝：pi_n（X，X_0） to check｛pi｝_n（X，X_0）$下的同伦群$check。子群$ker（Psi_n）$是该策略的障碍，因为它恰好由$pi_n（X，X_0）$的那些元素组成，这些元素不能通过$X$的多面体近似来检测。在本文中，我们使用Spanier基团的高维类似物来刻画$ker（Psi_n）$。特别地，我们证明了如果$X$是仿紧的，Hausdorff和$LC^｛n-1｝$，那么$ker（Psi_n）$等于$X$的第$n$个Spanier群。我们还利用高Spanier群的观点推广了Kozlowski Segal的一个定理，该定理给出了$Psi_{n}$是同构的条件。
{"title":"Elements of higher homotopy groups undetectable by polyhedral approximation","authors":"John K. Aceti, Jeremy Brazas","doi":"10.2140/pjm.2023.322.221","DOIUrl":"https://doi.org/10.2140/pjm.2023.322.221","url":null,"abstract":"When non-trivial local structures are present in a topological space $X$, a common approach to characterizing the isomorphism type of the $n$-th homotopy group $pi_n(X,x_0)$ is to consider the image of $pi_n(X,x_0)$ in the $n$-th v{C}ech homotopy group $check{pi}_n(X,x_0)$ under the canonical homomorphism $Psi_{n}:pi_n(X,x_0)to check{pi}_n(X,x_0)$. The subgroup $ker(Psi_n)$ is the obstruction to this tactic as it consists of precisely those elements of $pi_n(X,x_0)$, which cannot be detected by polyhedral approximations to $X$. In this paper, we use higher dimensional analogues of Spanier groups to characterize $ker(Psi_n)$. In particular, we prove that if $X$ is paracompact, Hausdorff, and $LC^{n-1}$, then $ker(Psi_n)$ is equal to the $n$-th Spanier group of $X$. We also use the perspective of higher Spanier groups to generalize a theorem of Kozlowski-Segal, which gives conditions ensuring that $Psi_{n}$ is an isomorphism.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48576450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.2140/pjm.2022.318.189
M. Sabitova
. We study certain subgroups G A of Q n defined by non-singular n × n -matrices A with integer coefficients. In the first non-trivial case when n = 2, we give necessary and sufficient conditions for two such groups to be isomorphic. Namely, in the generic case when the characteristic polynomial of A is irreducible, we attach a generalized ideal class to A and essentially, two groups are isomorphic if and only if the corresponding ideal classes are equivalent. The obtained results can be applied to studying associated toroidal solenoids.
{"title":"Generalized ideal classes in application to toroidal solenoids","authors":"M. Sabitova","doi":"10.2140/pjm.2022.318.189","DOIUrl":"https://doi.org/10.2140/pjm.2022.318.189","url":null,"abstract":". We study certain subgroups G A of Q n defined by non-singular n × n -matrices A with integer coefficients. In the first non-trivial case when n = 2, we give necessary and sufficient conditions for two such groups to be isomorphic. Namely, in the generic case when the characteristic polynomial of A is irreducible, we attach a generalized ideal class to A and essentially, two groups are isomorphic if and only if the corresponding ideal classes are equivalent. The obtained results can be applied to studying associated toroidal solenoids.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47225344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-14DOI: 10.2140/pjm.2022.317.363
Pingliang Huang, Youde Wang
. In this paper we consider the gradient estimates on positive solutions to the following elliptic equation defined on a complete Riemannian manifold ( M, g ):
． 本文研究了完全黎曼流形(M, g)上定义的椭圆方程正解的梯度估计:
{"title":"Gradient estimates and Liouville theorems for Lichnerowicz equations","authors":"Pingliang Huang, Youde Wang","doi":"10.2140/pjm.2022.317.363","DOIUrl":"https://doi.org/10.2140/pjm.2022.317.363","url":null,"abstract":". In this paper we consider the gradient estimates on positive solutions to the following elliptic equation defined on a complete Riemannian manifold ( M, g ):","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46363406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-13DOI: 10.2140/pjm.2023.324.157
Ziming Shi
Let $D$ be a bounded strictly pseudoconvex domain in $mathbb{C}^n$. Assuming $bD in C^{k+3+alpha}$ where $k$ is a non-negative integer and $0
设$D$是$mathbb{C}^n$中的一个有界严格伪凸域。假设$bD in C^{k+3+alpha}$，其中$k$是一个非负整数和$0
{"title":"Boundary regularity of Bergman kernel in\u0000Hölder space","authors":"Ziming Shi","doi":"10.2140/pjm.2023.324.157","DOIUrl":"https://doi.org/10.2140/pjm.2023.324.157","url":null,"abstract":"Let $D$ be a bounded strictly pseudoconvex domain in $mathbb{C}^n$. Assuming $bD in C^{k+3+alpha}$ where $k$ is a non-negative integer and $0<alpha leq 1$, we show that 1) the Bergman kernel $B(cdot, w_0) in C^{k+ min{alpha, frac12 } } (overline D)$, for any $w_0 in D$; 2) The Bergman projection on $D$ is a bounded operator from $C^{k+beta}(overline D)$ to $C^{k + min { alpha, frac{beta}{2} }}(overline D) $ for any $0<beta leq 1$. Our results both improve and generalize the work of E. Ligocka.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42603366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-09DOI: 10.2140/pjm.2023.324.333
G. Peruginelli
We show that every Dedekind domain $R$ lying between the polynomial rings $mathbb Z[X]$ and $mathbb Q[X]$ with the property that its residue fields of prime characteristic are finite fields is equal to a generalized ring of integer-valued polynomials, that is, for each prime $pinmathbb Z$ there exists a finite subset $E_p$ of transcendental elements over $mathbb Q$ in the absolute integral closure $overline{mathbb Z_p}$ of the ring of $p$-adic integers such that $R={finmathbb Q[X]mid f(E_p)subseteq overline{mathbb Z_p}, forall text{ prime }pinmathbb Z}$. Moreover, we prove that the class group of $R$ is isomorphic to a direct sum of a countable family of finitely generated abelian groups. Conversely, any group of this kind is the class group of a Dedekind domain $R$ between $mathbb Z[X]$ and $mathbb Q[X]$.
{"title":"Polynomial Dedekind domains with finite residue fields of prime characteristic","authors":"G. Peruginelli","doi":"10.2140/pjm.2023.324.333","DOIUrl":"https://doi.org/10.2140/pjm.2023.324.333","url":null,"abstract":"We show that every Dedekind domain $R$ lying between the polynomial rings $mathbb Z[X]$ and $mathbb Q[X]$ with the property that its residue fields of prime characteristic are finite fields is equal to a generalized ring of integer-valued polynomials, that is, for each prime $pinmathbb Z$ there exists a finite subset $E_p$ of transcendental elements over $mathbb Q$ in the absolute integral closure $overline{mathbb Z_p}$ of the ring of $p$-adic integers such that $R={finmathbb Q[X]mid f(E_p)subseteq overline{mathbb Z_p}, forall text{ prime }pinmathbb Z}$. Moreover, we prove that the class group of $R$ is isomorphic to a direct sum of a countable family of finitely generated abelian groups. Conversely, any group of this kind is the class group of a Dedekind domain $R$ between $mathbb Z[X]$ and $mathbb Q[X]$.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44660818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：