Rendiconti del Seminario Matematico
della Università di Padova
The Mathematical Journal of the University of Padua
e-ISSN: 2240-2926
Forthcoming Articles
(Last update: October 5, 2018)The following articles will soon be published in this journal.
Accepted Papers
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Cleanness of Cohen-Macaulay monomial ideal generated by at most five elements
Department of Mathematics College of Humanities and Sciences Nihon University 3-25-40 Sakurajosui Setagaya-ku Tokyo 156-8550 Japan yoshida@math.chs.nihon-u.ac.jp
Abstract: In this paper, we prove that any Cohen-Macaulay monomial ideal generated by at most five elements is clean.
received 13.10.2017, accepted 21.06.2018 (14 pages)
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The derived moduli stack of shifted symplectic structures
Department of Mathematics The University of British Columbia 1984 Mathematics Road, Vancouver, BC Canada V6T 1Z2 samuelbach@hotmail.fr Dipartimento di Matematica Universit… di Milano via Cesare Saldini 50 20133 Milano taly valerio.melani@unimi.it
Abstract: We introduce and study the derived moduli stack $\mathbb{Symp}(X,n)$ of $n$-shifted symplectic structures on a given derived stack $X$, as introduced in [8]. In particular, under reasonable assumptions on $X$, we prove that $\mathbb{Symp}(X,n)$ carries a canonical quadratic form, in the sense of [14]. This generalizes a classical result of Fricke and Habermann (see [3]), which was established in the $C^{\infty}$-setting, to the broader context of derived algebraic geometry, thus proving a conjecture stated in [14].
received 26.09.2017, accepted 15.06.2018 (16 pages)
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An addendum to the elliptic torsion anomalous conjecture in codimension 2
Mathematisches Institut Georg-August-Universit„t G”ttingen Bunsenstrasse 3-5 37073 G”ttingen Germany pevelina.viada@mathematik.uni-goettingen.deatrikh@gmx.ch further Viada Department of Mathematics ETH Zurich R„mistrasse 101, 8092 ZurichSwitzerland evelina.viada@math.ethz.ch
Abstract: The torsion anomalous conjecture states that for any variety $V$ in an abelian variety there are only finitely many maximal $V$-torsion anomalous varieties. We prove this conjecture for $V$ of codimension $2$ in a product $E^N$ of an elliptic curve $E$ without CM, complementing previous results for $E$ with CM. We also give an effective upper bound for the normalized height of these maximal $V$-torsion anomalous varieties.
received 30.01.2017, accepted 11.05.2018 (9 pages)
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Generating sets of Galois equivariant Krasner analytic functions
Department of Mathematics University of Bucharest 14 Academiei Street RO-010014 Bucharest Romania Simion Stoilow Institute of Mathematics of the Romanian Academy P.O. Box 1-764 RO-014700 Bucharest Romania Simion Stoilow Institute of Mathematics of the Romanian Academy P.O. Box 1-764 RO-014700 Bucharest Romania
Abstract: Given a prime number $p$ and $x$ an element of the Tate field $\mathbb{C}_p$, the main goal of the present paper is to provide an explicit generating set, which is given by the trace function of $x$ and all its derivatives, for the $\mathbb{C}_p$-Banach algebra of the Galois equivariant Krasner analytic functions defined on the complement in $\mathbb{P}^1(\mathbb{C}_p)$ of the orbit of $x$ with values in $\mathbb{C}_p$.
received 26.09.2017, accepted 13.03.2018 (14 pages)
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Nadler mappings in cone $b$-metric spaces over Banach algebras
Mathematics Yildiz Technical University 34210, Istanbul Turkey
Abstract: In this study we first define the concept of Nadler type contraction in the setting of $H$-cone $b$-metric space with respect to cone $b$-metric spaces over Banach algebras. Next we prove the Banach contraction principle for such contractions by means of the notion of spectral radius and a solid cone in underlying Banach algebra. Finally we observe that the main result achieved in this work extends and generalizes the well known results associated with contractions of Nadler type.
received 05.02.2018, accepted 12.03.2018 (10 pages)
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Structure d algebre de Gerstenhaber-Voronov sur les formes differentielles non commutatives
Institut pr‚paratoire aux ‚tudes d ing‚nieurs de Nabeul Universit‚ de Carthage Campus Universitaire Merazka, 8000 Nabeul Tunisie hatem_iaaoui@yahoo.com D‚partement des Math‚matiques Facult‚ des sciences de Tunis Universit‚ Tunis El Manar naoufelbattikh@yahoo.fr
Abstract: The algebra of noncommutative differential forms has been defined by A. Connes in }$\left[ 4\right] .$ Using this algebra, M. Karoubi has defined cyclic homology and Hochschild homology groups (see. $\left[ 13\right] $). These groups are related to the algebraic K-theory. The purpose of this paper is to provide the noncommutative differential forms algebra with the structure of Gerstenhaber-Voronov algebras.
received 13.06.2017, accepted 01.03.2018 (15 pages)
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On hypercentre-by-polycyclic-by-nilpotent groups
School of Mathematical Sciences Queen Mary University of London Mile End Road London E1 4NS England b.a.f.wehrfritz@qmul.ac.uk
Abstract: If $\{\gamma^{s+1}G\}$ and $\{\zeta_s(G)\}$ denote respectively the lower and upper central series of the group $G$, $s\ge 0$ an integer, and if $\gamma^{s+1}G/(\gamma^{s+1}G\cap\zeta_s(G))$ is polycyclic (resp. polycyclic-by-finite) for some $s$, then we prove that $G/\zeta_{2s}(G)$ is polycyclic (resp. polycyclic-by-finite). The corresponding result with polycyclic replaced by finite was proved in 2009 by G. A. Fern ndez-Alcober and M. Morigi. We also present an alternative approach to the latter.
received 25.08.2017, accepted 23.02.2018 (10 pages)
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On the singular spectrum of tempered ultrahyperfunctions corresponding to proper convex cones
Universidade Federal de Vi‡osa Departamento de Fisica Av. Peter Henry Rolfs s/n Campus Universitario Vi‡osa, MG Brasil, CEP: 36.570-900 daniel.franco@ufv.br universidade Federal de Juiz de Flora Departamento de Matematica Campus Universitario Bairro Martelos Juiz de Flora, MG Brasil, CEP: 36.036-900 magno_branco@yahoo.com.br
Abstract: We address in this paper the issue of singularities of ultrahyperfunctions. Following the Carmichael's approach for ultrahyperfunctions, we study the relation between the singular spectrum of a class of tempered ultrahyperfunctions corresponding to proper convex cones and their expressions as boundary values of holomorphic functions. In passing, a simple version of the celebrated edge of the wedge theorem for this setting is derived from the integral representation without using cohomology.
received 18.08.2017, accepted 09.02.2018 (17 pages)
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Twisted cyclic groups
Department of Mathematics and Statistics Youngstown State University One University Plaza Youngstown, OH 44555 United States
Abstract: A finite group $G$ is said to be \textsl{twisted cyclic} if there exist $\phi \in \text{Aut}(G)$ and $x \in G$ such that $G=\{(x^i)\phi^j\ :\ i,j \in \mathbb{Z}\}$. In this note, we classify all groups satisfying this property and determine that, if a finite group $G$ is twisted cyclic, then $G$ is isomorphic to $\mathbb{Z}_{p^n}$, $\mathbb{Z}_p\times \mathbb{Z}_p \times \cdots \times \mathbb{Z}_p$, $Q_8$, $\mathbb{Z}_{p^n}\times \mathbb{Z}_{p^n}$ or direct products of these groups for some prime $p$ and some $n\in \mathbb{Z}^{+}$.
received 03.01.2018, accepted 09.02.2018 (9 pages)
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On the values of unipotent characters in bad characteristic
IAZ - Lehrstuhl fr Algebra Universit„t Stuttgart Pfaffenwaldring 57 D-70569 Stuttgart Germany meinolf.geck@mathematik.uni-stuttgart.de
Abstract: Let $G(q)$ be a Chevalley group over a finite field $\F_q$. By Lusztig's and Shoji's work, the problem of computing the values of the unipotent characters of $G(q)$ is solved, in principle, by the theory of character sheaves; one issue in this solution is the determination of certain scalars relating two types of class functions on $G(q)$. We show that this issue can be reduced to the case where $q$ is a prime, which opens the way to use computer algebra methods. Here, and in a sequel to this article, we use this approach to solve a number of cases in groups of exceptional type which seemed hitherto out of reach.
received 24/01/2018, accepted 06.02.2018 (20 pages)
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Finite groups with the pp-embedding property
Institute of Mathematics University of Bialystok K. Ciolkowskiego 1M 15-245 Bialystok Poland
Abstract: A subset $X$ of a finite group $G$ is called g-independent if there is no proper subset $Y$ of $X$ such that $\langle Y,\Phi(G) \rangle = \langle X,\Phi(G) \rangle.$ The group $G$ has the embedding property if every g-independent subset of $G$ can be embedded in a minimal generating set of $G$. If $X$ is a set of prime power order elements, then we say that $G$ has the pp-embedding property. In this note we classify all finite solvable groups with the pp-embedding property. Moreover we prove that this class is equal to the class of finite solvable groups with the embedding property.
received 26.10.2017, accepted 19.01.2018 (11 pages)
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Regularity results for quasilinear degenerate elliptic obstacle problems in Carnot groups
Department of Applied Mathematics Northwestern Polytechnical University Xian China
Abstract: See the article
received 18.03.2017, accepted 09.12.2017 (32 pages)
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On the generalized $\sigma$-Fitting subgroup of finite groups
Hu, Huang School of Mathematics and Statistics Jiangsu Normal University Xuzhou, 221116 P. R. China Skiba Department of Mathematics Francisk Skorina Gomel State University Gomel 246019 Belarus
Abstract: see the article
received 26.02.2017, accepted 29.11.2017 (14 pages)
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On the monotonicity of Hilbert functions
Department of Mathematics Indian Institute of Technology Bombay Powai Mumbai 400 076 India
Abstract: In this paper we show that a large class of one-dimensional Cohen-Macaulay local rings $(A,\mathfrak{m})$ has the property that if $M$ is a maximal Cohen-Macaulay $A$-module then the Hilbert function of $M$ (with respect to $\mathfrak{m}$) is non-decreasing. Examples include
received 16.02.2017, accepted 09.11.2017 (7 pages)
(1) Complete intersections $A = Q/(f,g)$ where $(Q,\mathfrak{n})$ is regular local of dimension three and $f \in \mathfrak{n}^2 \setminus \mathfrak{n}^3$.
(2) One dimensional Cohen-Macaulay quotients of a two dimensional Cohen-Macaulay local ring with pseudo-rational singularity.
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Zeros of irreducible characters of metabelian $p$-groups
2 Amner Road London SW11 6AA UK
Abstract: We show that if $\chi$ is an irreducible complex character of a metabelian $p$ - group $P,$ where $p$ is an odd prime, and if $x\in P$ satisfies $\chi(x)\neq 0$, then the order of $x$ divides $|P|/\chi(1)^2.$
received 21.06.2017, accepted 09.11.2017 (9 pages)
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Cohen-Macaulayness and sequentially Cohen-Macaulayness of monomial ideals
Department of Mathematics Azarbaijan Shahid Madani University Tabriz Iran Department of Mathematics Razi University Kermanshah Iran
Abstract: In this paper, we give a characterization for Cohen--Macaulay rings $R/I$ where $I\subset R=K[y_1, \dots, y_n]$ is a monomial ideal which satisfies $\rm{bigsize}\, I=\rm{size}\, I$. Next, we let $S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]$ be a polynomial ring and $I\subset S$ a monomial ideal. We study the sequentially Cohen-Macaulayness of $S/I$ with respect to $Q=(y_1,\ldots,y_n)$. Moreover, if $I\subset R$ is a monomial ideal such that the associated prime ideals of $I$ are in pairwise disjoint sets of variables, a classification of $R/I$ to be sequentially Cohen-Macaulay is given. Finally, we compute $\rm{grade}\,(Q, M)$ where $M$ is a sequentially Cohen-Macaulay $S$-module with respect to $Q$.
received 02.04.2017, accepted 23.10.2017 (14 pages)
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On generalized $\Pi$-property of subgroups of finite groups
School of Mathematics Jilin University No. 2699 Qianjin Street Changchun China
Abstract: In this note, we extend the concept of $\Pi$-property of subgroups of finite groups and generalize some recent results. In particular, we generalize the main results of Li et al. [8] and Miao et al. [9].
received 28.08.2017, accepted 23.10.2017 (17 pages)
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On the uniqueness of the factorization of power digraphs modulo n
Department of Mathematics North-Eastern Hill University Shillong-793022 India Department of Basic Sciences & Social Sciences North-Eastern Hill University Shillong-793022 India
Abstract: For each pair of integers $n=\prod_{i=1}^{r}p_i^{e_i}$ and $k \geq 2$, a digraph $G(n,k)$ is one with vertex set $\{0,1,\ldots ,n-1\}$ and for which there exists a directed edge from $x$ to $y$ if $x^k \equiv y \pmod n$. Using the Chinese Remainder Theorem, the digraph $G(n,k)$ can be written as a direct product of digraphs $G(p_i^{e_i},k)$ for all $i$ such that $1 \leq i \leq r$. A fundamental constituent $G_{P}^{*}(n,k)$, where $P \subseteq Q=\{p_1,p_2,\ldots,p_r\}$, is a subdigraph of $G(n,k)$ induced on the set of vertices which are multiples of $\prod_{{p_i} \in P}p_i$ and are relatively prime to all primes $p_j \in Q \smallsetminus P$. In this paper, we investigate the uniqueness of the factorization of trees attached to cycle vertices of the type $0$, $1$, and $(1,0)$, and in general, the uniqueness of $G(n,k)$. Moreover, we provide a necessary and sufficient condition for the isomorphism of the fundamental constituents $G_{P}^{*}(n,k_1)$ and $G_{P}^{*}(n,k_2)$ of $G(n,k_1)$ and $G(n,k_2)$ respectively for $k_1 \neq k_2$.
received 01.06.2017, accepted 20.10.2017 (28 pages)
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Semisimple groups that are quasi-split over a tamely ramified extension
Université Claude Bernard Lyon 1 CNRS UMR 5208 Institut Camille Jordan 43 Blvd. du 11 novembre 1918 F-69622 Villeurbane cedex France
Abstract: Let $K$ be a discretly henselian field whose residue field is separably closed. Answering a question raised by G. Prasad, we show that a semisimple $K$-group $G$ is quasi-split if and only if it quasi-splits after a finite tamely ramified extension of $K$.
received 07.07.2017, accepted 16.10.2017 (9 pages)
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Complex manifolds as families of homotopy algebras
Institut de Mathématiques de Toulouse UMR5219, Université de Toulouse CNRS, UPS IMT F-31062 Toulouse Cedex 9 France
Abstract: We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex structure on a smooth manifold corresponds in this way to a family of algebras indexed by the points of the manifold.
received 24.03.2017, accepted 25.09.2017 (38 pages)
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A brief journey through extensions of rational groups
University of Stralsund Zur Schwedenschanze 15 18435 Stralsund Germany
Abstract: Let $A$ and $B$ be rational groups, i.e. torsion-free groups of rank-1 and thus subgroups of the rational numbers. This paper gives a short overview of the structure of $\text{Ext}\,(A,B)$ especially considering some interesting classes of torsion-free pairs.
received 06.03.2017, accepted 20.09.2017 (5 pages)
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Algebraic cycles on a very special EPW sextic
Institut de Recherche Mathématique Avancée CNRS _ Université de Strasbourg 7 Rue René Descartes 67084 Strasbourg CEDEX France
Abstract: Motivated by the Beauville--Voisin conjecture about Chow rings of powers of $K3$ surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of this conjecture for the very special EPW sextic studied by Donten--Bury et alii. We also prove some other results concerning the Chow groups of this very special EPW sextic, and of certain related hyperk\"ahler fourfolds.
received 22.06.2016, accepted 28.08.2017 (27 pages)
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Countable recognizability and residual properties of groups
Dipartimento di Matematica e Applicazioni Università di Napoli Federico II Complesso Universitario Monte S. Angelo Via Cintia, Napoli Italy
Abstract: A class of groups {\mgoth X} is said to be countably recognizable if a group belongs to~{\mgoth X} whenever all its countable subgroups lie in {\mgoth X}. It is proved here that the class of groups whose subgroups are closed in the profinite topology is countably recognizable. Moreover, countably detectable properties of the finite residual of a group are studied.
received 17.01.2017, accepted 29.05.2017 (11 pages)
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A result on a singular Cauchy problem with a radial point revisited using microdifferential calculus
Department of Mathematics Edificio Mario Laserna Cra 1 Este No 19A 40 Bogota Colombia Universidad de los Andes Colombia
Abstract: We study the ramified Cauchy problem for a linear PDE with a radial point using the theory of microdifferential operators.
received 23.09.2016, accepted 11.05.2017 (20 pages)
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Mostow s fibration for canonical embeddings of compact homogeneous $CR$ manifolds
Dipartimento di Matematica e Fisica III Università di Roma Largo San Leonardo Murialdo, 1 00146 Roma Italy Dipartimento di Matematica II Università di Roma “Tor Vergata” Via della Ricerca Scientifica 00133 Roma Italy
Abstract: We define a class of compact homogeneous $CR$ manifolds which are bases of Mostow fibrations having total spaces equal to their canonical complex realizations and Hermitian fibers. This is used to establish isomorphisms between their tangential Cauchy-Riemann cohomology groups and the corresponding Dolbeault cohomology groups of the embeddings.
received 17.12.2016, accepted 09.05.2017 (30 pages)
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