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A NOTE ON RATIONAL HOMOLOGICAL STABILITY OF AUTOMORPHISMS OF MANIFOLDS 流形自同构的有理同调稳定性的一个注记
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmathj/haaa017
Manuel Krannich
{"title":"A NOTE ON RATIONAL HOMOLOGICAL STABILITY OF AUTOMORPHISMS OF MANIFOLDS","authors":"Manuel Krannich","doi":"10.1093/qmathj/haaa017","DOIUrl":"https://doi.org/10.1093/qmathj/haaa017","url":null,"abstract":"By work of Berglund and Madsen, the rings of rational characteristic classes of fibrations and smooth block bundles with fibre \u0000<tex>$D^{2n}sharp (S^ntimes S^n)^{sharp g}$</tex>\u0000, relative to the boundary, are for \u0000<tex>$2nge 6$</tex>\u0000 independent of \u0000<tex>$g$</tex>\u0000 in degrees \u0000<tex>$*le (g-6)/2$</tex>\u0000. In this note, we explain how this range can be improved to \u0000<tex>$*le g-2$</tex>\u0000 using cohomological vanishing results due to Borel and the classical invariant theory. This implies that the analogous ring for smooth bundles is independent of \u0000<tex>$g$</tex>\u0000 in the same range, provided the degree is small compared to the dimension.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haaa017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49967015","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}
引用次数: 4
The Composition Operation on Spaces of Holomorphic Mappings 全纯映射空间上的复合运算
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmathj/haz035
María D Acosta;Pablo Galindo;Luiza A Moraes
{"title":"The Composition Operation on Spaces of Holomorphic Mappings","authors":"María D Acosta;Pablo Galindo;Luiza A Moraes","doi":"10.1093/qmathj/haz035","DOIUrl":"https://doi.org/10.1093/qmathj/haz035","url":null,"abstract":"We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haz035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49989716","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}
引用次数: 0
Flat ring epimorphisms and universal localizations of commutative rings 交换环的平环附子与泛定域
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmath/haaa041
Lidia Angeleri Hügel;Frederik Marks;Jan Št’ovíček;Ryo Takahashi;Jorge Vitória
{"title":"Flat ring epimorphisms and universal localizations of commutative rings","authors":"Lidia Angeleri Hügel;Frederik Marks;Jan Št’ovíček;Ryo Takahashi;Jorge Vitória","doi":"10.1093/qmath/haaa041","DOIUrl":"https://doi.org/10.1093/qmath/haaa041","url":null,"abstract":"We study different types of localizations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring epimorphism is a universal localization in the sense of Cohn and Schofield; and (b) when such universal localizations are classical rings of fractions. In order to find such criteria, we use the theory of support and we analyse the specialization closed subset associated to a flat ring epimorphism. In case the underlying ring is locally factorial or of Krull dimension one, we show that all flat ring epimorphisms are universal localizations. Moreover, it turns out that an answer to the question of when universal localizations are classical depends on the structure of the Picard group. We furthermore discuss the case of normal rings, for which the divisor class group plays an essential role to decide if a given flat ring epimorphism is a universal localization. Finally, we explore several (counter)examples which highlight the necessity of our assumptions.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haaa041","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49966432","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}
引用次数: 15
DEFORMATION THEORY OF THE CHOW GROUP OF ZERO CYCLES 零循环周氏群的变形理论
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmathj/haaa004
Morten Lüders
{"title":"DEFORMATION THEORY OF THE CHOW GROUP OF ZERO CYCLES","authors":"Morten Lüders","doi":"10.1093/qmathj/haaa004","DOIUrl":"https://doi.org/10.1093/qmathj/haaa004","url":null,"abstract":"We study the deformations of the Chow group of zerocycles of the special fibre of a smooth scheme over a Henselian discrete valuation ring. Our main tools are Bloch's formula and differential forms. As a corollary we get an algebraization theorem for thickened zero cycles previously obtained using idelic techniques. In the course of the proof we develop moving lemmata and Lefschetz theorems for cohomology groups with coefficients in differential forms.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haaa004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49966581","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}
引用次数: 2
IDEAL ZETA FUNCTIONS ASSOCIATED TO A FAMILY OF CLASS-2-NILPOTENT LIE RINGS 一类2类幂零李环的理想ζ函数
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmathj/haaa010
Christopher Voll
{"title":"IDEAL ZETA FUNCTIONS ASSOCIATED TO A FAMILY OF CLASS-2-NILPOTENT LIE RINGS","authors":"Christopher Voll","doi":"10.1093/qmathj/haaa010","DOIUrl":"https://doi.org/10.1093/qmathj/haaa010","url":null,"abstract":"We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-\u0000<tex>$2$</tex>\u0000-nilpotent Lie rings, introduced in M. N. Berman, B. Klopsch and U. Onn (A family of class-2 nilpotent groups, their automorphisms and pro-isomorphic zeta functions, Math. Z. 290 (2018), 909935), in terms of Igusa functions. As corollaries we obtain information about analytic properties of global ideal zeta functions, local functional equations, topological, reduced and graded ideal zeta functions, as well as representation zeta functions for the unipotent group schemes associated to the Lie rings in question.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haaa010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49966587","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}
引用次数: 5
Hardy Spaces on Homogeneous Groups and Littlewood-Paley Functions 齐次群上的Hardy空间与Littlewood-Paley函数
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmath/haz049
Shuichi Sato
{"title":"Hardy Spaces on Homogeneous Groups and Littlewood-Paley Functions","authors":"Shuichi Sato","doi":"10.1093/qmath/haz049","DOIUrl":"https://doi.org/10.1093/qmath/haz049","url":null,"abstract":"We establish a characterization of the Hardy spaces on the homogeneous groups in terms of the Littlewood–Paley functions. The proof is based on vector-valued inequalities shown by applying the Peetre maximal function.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haz049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49982464","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}
引用次数: 3
Erratum to: Sums of Linear Transformations in Higher Dimensions 对:高维线性变换和的勘误
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmath/haz023
{"title":"Erratum to: Sums of Linear Transformations in Higher Dimensions","authors":"","doi":"10.1093/qmath/haz023","DOIUrl":"https://doi.org/10.1093/qmath/haz023","url":null,"abstract":"","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haz023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49982468","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}
引用次数: 0
Short Character Sums and the Pólya–Vinogradov Inequality 短字符和和Pólya-Vinogradov不等式
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmath/haaa031
Alexander P Mangerel
{"title":"Short Character Sums and the Pólya–Vinogradov Inequality","authors":"Alexander P Mangerel","doi":"10.1093/qmath/haaa031","DOIUrl":"https://doi.org/10.1093/qmath/haaa031","url":null,"abstract":"We show in a quantitative way that any odd primitive character χ modulo q of fixed order g ≥ 2 satisfies the property that if the Pólya–Vinogradov inequality for χ can be improved to \u0000<tex>$$begin{equation*} max_{1 leq t leq q} left|sum_{n leq t} chi(n)right| = o_{q rightarrow infty}(sqrt{q}log q) end{equation*}$$</tex>\u0000 then for any ɛ > 0 one may exhibit cancellation in partial sums of χ on the interval [1, t] whenever \u0000<tex>$t gt q^{varepsilon}$</tex>\u0000, i.e., \u0000<tex>$$begin{equation*} sum_{n leq t} chi(n) = o_{q rightarrow infty}(t) text{for all } t gt q^{varepsilon}. end{equation*}$$</tex>\u0000 We also prove a converse implication, to the effect that if all odd primitive characters of fixed order dividing g exhibit cancellation in short sums then the Pólya–Vinogradov inequality can be improved for all odd primitive characters of order g. Some applications are also discussed.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49982471","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}
引用次数: 6
A Sharp Adams-Type Inequality for Weighted Sobolev Spaces 加权Sobolev空间的一个Sharp adams型不等式
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmathj/haz051
João Marcos do Ó;Abiel Costa Macedo;José Francisco de Oliveira
{"title":"A Sharp Adams-Type Inequality for Weighted Sobolev Spaces","authors":"João Marcos do Ó;Abiel Costa Macedo;José Francisco de Oliveira","doi":"10.1093/qmathj/haz051","DOIUrl":"10.1093/qmathj/haz051","url":null,"abstract":"In a classical work (Ann. Math.128, (1988) 385–398), D. R. Adams proved a sharp Trudinger–Moser inequality for higher-order derivatives. We derive a sharp Adams-type inequality and Sobolev-type inequalities associated with a class of weighted Sobolev spaces that is related to a Hardy-type inequality.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haz051","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47876344","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}
引用次数: 11
POINCARÉ DUALITY, CAP PRODUCT AND BOREL–MOORE INTERSECTION HOMOLOGY PoincarÉ对偶性，帽积和borel-moore交同调
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2020-03-01 DOI: 10.1093/qmathj/haaa009
Martintxo Saralegi-Aranguren;Daniel Tanré
{"title":"POINCARÉ DUALITY, CAP PRODUCT AND BOREL–MOORE INTERSECTION HOMOLOGY","authors":"Martintxo Saralegi-Aranguren;Daniel Tanré","doi":"10.1093/qmathj/haaa009","DOIUrl":"10.1093/qmathj/haaa009","url":null,"abstract":"Using a cap product, we construct an explicit Poincaré duality isomorphism between the blown-up intersection cohomology and the Borel–Moore intersection homology, for any commutative ring of coefficients and second-countable, oriented pseudomanifolds.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haaa009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46931832","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}
引用次数: 7
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