Nagoya Mathematical Journal最新文献_第9页

ON THE MILNOR FIBRATION OF CERTAIN NEWTON DEGENERATE FUNCTIONS 关于某些牛顿退化函数的MILNOR FIBRATION

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-08-18 DOI: 10.1017/nmj.2022.37

C. Eyral, M. Oka

引用次数: 0

LIE ALGEBRA MODULES WHICH ARE LOCALLY FINITE AND WITH FINITE MULTIPLICITIES OVER THE SEMISIMPLE PART 局部有限且在半单部分上具有有限复数的李代数模

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-08-02 DOI: 10.1017/nmj.2021.8

V. Mazorchuk, Rafael Mrðen

{"title":"LIE ALGEBRA MODULES WHICH ARE LOCALLY FINITE AND WITH FINITE MULTIPLICITIES OVER THE SEMISIMPLE PART","authors":"V. Mazorchuk, Rafael Mrðen","doi":"10.1017/nmj.2021.8","DOIUrl":"https://doi.org/10.1017/nmj.2021.8","url":null,"abstract":"Abstract For a finite-dimensional Lie algebra \u0000$mathfrak {L}$\u0000 over \u0000$mathbb {C}$\u0000 with a fixed Levi decomposition \u0000$mathfrak {L} = mathfrak {g} ltimes mathfrak {r}$\u0000 , where \u0000$mathfrak {g}$\u0000 is semisimple, we investigate \u0000$mathfrak {L}$\u0000 -modules which decompose, as \u0000$mathfrak {g}$\u0000 -modules, into a direct sum of simple finite-dimensional \u0000$mathfrak {g}$\u0000 -modules with finite multiplicities. We call such modules \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules. We give a complete classification of simple \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules for the Takiff Lie algebra associated to \u0000$mathfrak {g} = mathfrak {sl}_2$\u0000 , and for the Schrödinger Lie algebra, and obtain some partial results in other cases. An adapted version of Enright’s and Arkhipov’s completion functors plays a crucial role in our arguments. Moreover, we calculate the first extension groups of infinite-dimensional simple \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules and their annihilators in the universal enveloping algebra, for the Takiff \u0000$mathfrak {sl}_2$\u0000 and the Schrödinger Lie algebra. In the general case, we give a sufficient condition for the existence of infinite-dimensional simple \u0000$mathfrak {g}$\u0000 -Harish-Chandra modules.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87837443","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}

引用次数: 4

IWASAWA THEORY FOR p-TORSION CLASS GROUP SCHEMES IN CHARACTERISTIC p 特征p-扭转类群方案的IWASAWA理论

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-07-27 DOI: 10.1017/nmj.2022.30

J. Booher, Bryden Cais

{"title":"IWASAWA THEORY FOR p-TORSION CLASS GROUP SCHEMES IN CHARACTERISTIC p","authors":"J. Booher, Bryden Cais","doi":"10.1017/nmj.2022.30","DOIUrl":"https://doi.org/10.1017/nmj.2022.30","url":null,"abstract":"Abstract We investigate a novel geometric Iwasawa theory for \u0000${mathbf Z}_p$\u0000 -extensions of function fields over a perfect field k of characteristic \u0000$p>0$\u0000 by replacing the usual study of p-torsion in class groups with the study of p-torsion class group schemes. That is, if \u0000$cdots to X_2 to X_1 to X_0$\u0000 is the tower of curves over k associated with a \u0000${mathbf Z}_p$\u0000 -extension of function fields totally ramified over a finite nonempty set of places, we investigate the growth of the p-torsion group scheme in the Jacobian of \u0000$X_n$\u0000 as \u0000$nrightarrow infty $\u0000 . By Dieudonné theory, this amounts to studying the first de Rham cohomology groups of \u0000$X_n$\u0000 equipped with natural actions of Frobenius and of the Cartier operator V. We formulate and test a number of conjectures which predict striking regularity in the \u0000$k[V]$\u0000 -module structure of the space \u0000$M_n:=H^0(X_n, Omega ^1_{X_n/k})$\u0000 of global regular differential forms as \u0000$nrightarrow infty .$\u0000 For example, for each tower in a basic class of \u0000${mathbf Z}_p$\u0000 -towers, we conjecture that the dimension of the kernel of \u0000$V^r$\u0000 on \u0000$M_n$\u0000 is given by \u0000$a_r p^{2n} + lambda _r n + c_r(n)$\u0000 for all n sufficiently large, where \u0000$a_r, lambda _r$\u0000 are rational constants and \u0000$c_r : {mathbf Z}/m_r {mathbf Z} to {mathbf Q}$\u0000 is a periodic function, depending on r and the tower. To provide evidence for these conjectures, we collect extensive experimental data based on new and more efficient algorithms for working with differentials on \u0000${mathbf Z}_p$\u0000 -towers of curves, and we prove our conjectures in the case \u0000$p=2$\u0000 and \u0000$r=1$\u0000 .","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43187510","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}

引用次数: 3

POSITIVELY CURVED FINSLER METRICS ON VECTOR BUNDLES 向量束上的正弯曲finsler度量

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-07-01 DOI: 10.1017/nmj.2022.2

Kuang-Ru Wu

引用次数: 1

POWER SERIES PROOFS FOR LOCAL STABILITIES OF KÄHLER AND BALANCED STRUCTURES WITH MILD $partial overline {partial }$ -LEMMA 具有MILD$partialoverline{partial}$-LEMA的KöHLER和平衡结构局部稳定性的幂级数证明

IF 0.8 2区数学

Nagoya Mathematical Journal Pub Date : 2021-06-08 DOI: 10.1017/nmj.2021.4

S. Rao, Xueyuan Wan, Quanting Zhao