{"title":"On the Structure of the Galois Group of the Maximal Pro-$p$ Extension with Restricted Ramification over the Cyclotomic $mathbb{Z}_p$-extension","authors":"T. Itoh","doi":"10.3836/TJM/1502179301","DOIUrl":"https://doi.org/10.3836/TJM/1502179301","url":null,"abstract":"Let $k_infty$ be the cyclotomic $mathbb{Z}_p$-extension of an algebraic number field $k$. We denote by $S$ a finite set of prime numbers which does not contain $p$, and $S(k_infty)$ the set of primes of $k_infty$ lying above $S$. In the present paper, we will study the structure of the Galois group $mathcal{X}_S (k_infty)$ of the maximal pro-$p$ extension unramified outside $S (k_infty)$ over $k_infty$. We mainly consider the question whether $mathcal{X}_S (k_infty)$ is a non-abelian free pro-$p$ group or not. In the former part, we treat the case when $k$ is an imaginary quadratic field and $S = emptyset$ (here $p$ is an odd prime number which does not split in $k$). In the latter part, we treat the case when $k$ is a totally real field and $S neq emptyset$.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48658246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a Rationality Problem for Fields of Cross-ratios","authors":"Z. Reichstein","doi":"10.3836/TJM/1502179305","DOIUrl":"https://doi.org/10.3836/TJM/1502179305","url":null,"abstract":"Let k be a field, x1, . . . , xn be independent variables and Ln = k(x1, . . . , xn). The symmetric group Σn acts on Ln by permuting the variables, and the projective linear group PGL2 acts by","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Unique Solvability of Nonlinear Fuchsian Partial Differential Equations","authors":"Dennis B. Bacani, J. Lope, H. Tahara","doi":"10.3836/TJM/1502179268","DOIUrl":"https://doi.org/10.3836/TJM/1502179268","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44457936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Non-existence of Static Pluriclosed Metrics on Non-Kähler Minimal Complex Surfaces","authors":"Masaya Kawamura","doi":"10.3836/TJM/1502179255","DOIUrl":"https://doi.org/10.3836/TJM/1502179255","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49373806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic Behavior of Solutions to the One-dimensional Keller-Segel System with Small Chemotaxis","authors":"Yumi Yahagi","doi":"10.3836/TJM/1502179267","DOIUrl":"https://doi.org/10.3836/TJM/1502179267","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41762649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Semi-simple Case of the Galois Brumer-Stark Conjecture for Monomial Groups","authors":"Xavier-François Roblot","doi":"10.3836/TJM/1502179243","DOIUrl":"https://doi.org/10.3836/TJM/1502179243","url":null,"abstract":"In a previous work, we stated a conjecture, called the Galois Brumer-Stark conjecture, that generalizes the (abelian) Brumer-Stark conjecture to Galois extensions. Other generalizations of the Brumer-Stark conjecture to non-abelian Galois extensions are due to Nickel. Nomura proved that the Brumer-Stark conjecture implies the weak non-abelian Brumer-Stark conjecture of Nickel when the group is monomial. In this paper, we use the methods of Nomura to prove that the Brumer-Stark conjecture implies the Galois Brumer-Stark conjecture for monomial groups in the semi-simple case.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41402922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Diffusion Process with a Random Potential Consisting of Two Contracted Self-Similar Processes","authors":"Yukiharu Suzuki","doi":"10.3836/TJM/1502179248","DOIUrl":"https://doi.org/10.3836/TJM/1502179248","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44024585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Symmetric Spaces Associated to Classical Groups with Even Characteristic","authors":"Junbin Dong, T. Shoji, Gao Yang","doi":"10.3836/tjm/1502179368","DOIUrl":"https://doi.org/10.3836/tjm/1502179368","url":null,"abstract":"Let $G = GL(V)$ for an N-dimensional vector space $V$ over an algebraically closed field k, and $G^{theta}$ the fixed point subgroup of $G$ under an involution $theta$ on $G$. In the case where $G^{theta} = O(V)$, the generalized Springer correspondence for the unipotent variety of the symmetric space $G/G^{theta}$ was studied by last two authors, under the assumption that ch k is odd. The definition of $theta$, and of the associated symmetric space given there make sense even if ch k = 2. In this paper, we discuss the Springer correspondence for those symmetric spaces of even characteristic. We show that if N is even, the Springer correspondence is reduced to that of symplectic Lie algebras in ch k = 2, which was determined by Xue. While if N is odd, we show that a very similar phenomenon as in the case of exotic symmetric space of level 3 appears.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42095884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Singular Locus of an Almost Distance Function","authors":"Minoru Tanaka","doi":"10.3836/TJM/1502179298","DOIUrl":"https://doi.org/10.3836/TJM/1502179298","url":null,"abstract":"The aim of this article is to generalize the notion of the cut locus and to get the structure theorem for it. For this purpose, we first introduce a class of 1-Lipschitz functions, each member of which is called an {it almost distance function}. Typical examples of an almost distance function are the distance function from a point and the Busman function on a complete Riemannian manifold. The generalized notion of the cut locus in this paper is called the {it singular locus} of an almost distance function. The singular locus consists of the upper one and the lower one. The upper singular locus coincides with the cut locus of a point for the distance function from the point, and the lower singular locus coincides with the set of all copoints of a ray when the almost distance function is the Busman function of the ray. Therefore, it is possible to treat the cut locus of a closed subset and the set of copoints of a ray in a unified way by introducing the singular locus for the almost distance function. In this article, we obtain the structure theorem (Theorem B) for the singular locus of an almost distance function on a 2-dimensional Finsler manifold that contains both structure theorems ([S], Theorem B) and [Sa,Theorem 2.13]) for the cut locus and the set of copoints of a ray as a corollary.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41357041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quasi-isometric Embeddings from Generalised Thompson’s Groups to Thompson’s Group T","authors":"Xiaobing Sheng","doi":"10.3836/tjm/1502179371","DOIUrl":"https://doi.org/10.3836/tjm/1502179371","url":null,"abstract":"Brown has defined the generalised Thompson's group $F_n$, $T_n$, where $n$ is an integer at least $2$ and Thompson's groups $F= F_2$ and $T =T_2$ in the 80's. Burillo, Cleary and Stein have found that there is a quasi-isometric embedding from $F_n$ to $F_m$ where $n$ and $m$ are positive integers at least 2. We show that there is a quasi-isometric embedding from $T_n$ to $T_2$ for any $n geq 2$ and no embeddings from $T_2$ to $T_n$ for $n geq 3$.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46696067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}