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Rendiconti del Seminario Matematico
della Università di Padova
The Mathematical Journal of the University of Padua

ISSN 0041-8994
e-ISSN: 2240-2926

Forthcoming Articles

(Last update: October 5, 2018)

The following articles will soon be published in this journal.

To view the abstract, or download the full paper in PDF[1], click on the article's title.

Accepted Papers

  • Cleanness of Cohen-Macaulay monomial ideal generated by at most five elements

    Enomoto, Chihiro and Yoshida, Ken-ichi
    Department of Mathematics
    College of Humanities and Sciences
    Nihon University
    3-25-40 Sakurajosui
    Tokyo 156-8550

    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)
    download: manuscript pdf (120K)
  • The derived moduli stack of shifted symplectic structures

    Bach, Samuel and Melani, Valerio
    Department of Mathematics
    The University of British Columbia
    1984 Mathematics Road, Vancouver, BC
    Canada V6T 1Z2
    Dipartimento di Matematica Universit… di Milano
    via Cesare Saldini 50
    20133 Milano

    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)
    download: manuscript pdf (328K)
  • An addendum to the elliptic torsion anomalous conjecture in codimension 2

    Hubschmid, Patrik and Viada, Evelina
    Mathematisches Institut
    Georg-August-Universit„t G”ttingen
    Bunsenstrasse 3-5
    37073 G”ttingen
    further Viada
    Department of Mathematics
    ETH Zurich
    R„mistrasse 101,
    8092 ZurichSwitzerland

    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)
    download: manuscript pdf (265K)
  • Generating sets of Galois equivariant Krasner analytic functions

    Alexandru, Victor and Vajaitu, Marian and Zaharescu, Alexandru
    Department of Mathematics
    University of Bucharest
    14 Academiei Street
    RO-010014 Bucharest
    Simion Stoilow Institute of Mathematics of the Romanian Academy
    P.O. Box 1-764
    RO-014700 Bucharest
    Simion Stoilow Institute of Mathematics of the Romanian Academy
    P.O. Box 1-764
    RO-014700 Bucharest

    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)
    download: manuscript pdf (295K)
  • Nadler mappings in cone $b$-metric spaces over Banach algebras

    Ozavsar, Muttalip
    Yildiz Technical University
    34210, Istanbul

    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)
    download: manuscript pdf (295K)
  • Structure d algebre de Gerstenhaber-Voronov sur les formes differentielles non commutatives

    Issaoui, Hatem and Battikh, Naoufel
    Institut pr‚paratoire aux ‚tudes d ing‚nieurs de Nabeul
    Universit‚ de Carthage
    Campus Universitaire
    Merazka, 8000
    D‚partement des Math‚matiques
    Facult‚ des sciences de Tunis
    Universit‚ Tunis El Manar

    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)
    download: manuscript pdf (340K)
  • On hypercentre-by-polycyclic-by-nilpotent groups

    Wehrfritz, B. A. F.
    School of Mathematical Sciences
    Queen Mary University of London
    Mile End Road
    London E1 4NS

    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)
    download: manuscript pdf (127K)
  • On the singular spectrum of tempered ultrahyperfunctions corresponding to proper convex cones

    Franco, Daniel H. T. and Alves, Magno B.
    Universidade Federal de Vi‡osa
    Departamento de Fisica 
    Av. Peter Henry Rolfs s/n
    Campus Universitario
    Vi‡osa, MG
    Brasil, CEP: 36.570-900
    universidade Federal de Juiz de Flora
    Departamento de Matematica
    Campus Universitario
    Bairro Martelos
    Juiz de Flora, MG
    Brasil, CEP: 36.036-900

    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)
    download: manuscript pdf (467K)
  • Twisted cyclic groups

    Flowers, Neil and Wakefield, Thomas
    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)
    download: manuscript pdf (356K)
  • On the values of unipotent characters in bad characteristic

    Geck, Meinolf
    IAZ - Lehrstuhl fr Algebra
    Universit„t Stuttgart
    Pfaffenwaldring 57
    D-70569 Stuttgart

    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)
    download: manuscript pdf (303K)
  • Finite groups with the pp-embedding property

    Stocka, Agnieszka
    Institute of Mathematics
    University of Bialystok
    K. Ciolkowskiego 1M
    15-245 Bialystok

    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)
    download: manuscript pdf (296K)
  • Regularity results for quasilinear degenerate elliptic obstacle problems in Carnot groups

    Du, Guangwei and Niu, Pengcheng and Han, Junqiang
    Department of Applied Mathematics
    Northwestern Polytechnical University

    Abstract: See the article

    received 18.03.2017, accepted 09.12.2017 (32 pages)
    download: manuscript pdf (464K)
  • On the generalized $\sigma$-Fitting subgroup of finite groups

    Hu, Bin and Huang, Jianhong and Skiba, Alexander N.
    Hu, Huang
    School of Mathematics and Statistics
    Jiangsu Normal University
    Xuzhou, 221116
    P. R. China
    Department of Mathematics
    Francisk Skorina Gomel State University
    Gomel 246019

    Abstract: see the article

    received 26.02.2017, accepted 29.11.2017 (14 pages)
    download: manuscript pdf (234K)
  • On the monotonicity of Hilbert functions

    Puthenpurakal, Tony Joseph
    Department of Mathematics
    Indian Institute of Technology Bombay
    Mumbai 400 076

    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
    (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.

    received 16.02.2017, accepted 09.11.2017 (7 pages)
    download: manuscript pdf (248K)
  • Zeros of irreducible characters of metabelian $p$-groups

    Wilde, Tom
    2 Amner Road
    London SW11 6AA

    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)
    download: manuscript pdf (304K)
  • Cohen-Macaulayness and sequentially Cohen-Macaulayness of monomial ideals

    Noormohammadi, Hassan and Rahimi, Ahad
    Department of Mathematics
    Azarbaijan Shahid Madani University
    Department of Mathematics
    Razi University

    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)
    download: manuscript pdf (323K)
  • On generalized $\Pi$-property of subgroups of finite groups

    Yu, Haoran
    School of Mathematics
    Jilin University
    No. 2699 Qianjin Street

    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)
    download: manuscript pdf (345K)
  • On the uniqueness of the factorization of power digraphs modulo n

    Sawkmie, Amplify and Singh, Madan Mohan
    Department of Mathematics
    North-Eastern Hill University
    Department of Basic Sciences & Social Sciences
    North-Eastern Hill University

    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)
    download: manuscript pdf (460K)
  • Semisimple groups that are quasi-split over a tamely ramified extension

    Gille, Philippe
    Université Claude Bernard Lyon 1
    CNRS UMR 5208
    Institut Camille Jordan
    43 Blvd. du 11 novembre 1918
    F-69622 Villeurbane cedex

    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)
    download: manuscript pdf (318K)
  • Complex manifolds as families of homotopy algebras

    Bellier-Millès, Joan
    Institut de Mathématiques de Toulouse
    UMR5219, Université de Toulouse
    F-31062 Toulouse Cedex 9

    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)
    download: manuscript pdf (538K)
  • A brief journey through extensions of rational groups

    Friedenberg, Stefan
    University of Stralsund
    Zur Schwedenschanze 15
    18435 Stralsund

    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)
    download: manuscript pdf (272K)
  • Algebraic cycles on a very special EPW sextic

    Laterveer, Robert
    Institut de Recherche Mathématique Avancée
    CNRS _ Université de Strasbourg
    7 Rue René Descartes
    67084 Strasbourg CEDEX

    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)
    download: manuscript pdf (320K)
  • Countable recognizability and residual properties of groups

    De Giovanni, Francesco and Trombetti, Marco
    Dipartimento di Matematica e Applicazioni
    Università di Napoli Federico II
    Complesso Universitario Monte S. Angelo
    Via Cintia,

    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)
    download: manuscript pdf (306K)
  • A result on a singular Cauchy problem with a radial point revisited using microdifferential calculus

    Getmanenko, Alexander
    Department of Mathematics
    Edificio Mario Laserna Cra 1 Este No 19A
    40 Bogota
    Universidad de los Andes

    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)
    download: manuscript pdf (447K)
  • Mostow s fibration for canonical embeddings of compact homogeneous $CR$ manifolds

    Marini, Stefano and Nacinovich, Mauro
    Dipartimento di Matematica e Fisica
    III Università di Roma
    Largo San Leonardo Murialdo, 1
    00146 Roma
    Dipartimento di Matematica
    II Università di Roma “Tor Vergata”
    Via della Ricerca Scientifica
    00133 Roma

    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)
    download: manuscript pdf (278K)

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