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European Mathematical Society Publishing House
2024-03-29 08:54:26
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RSMUP&vol=127&update_since=2024-03-29
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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127
2012
0
On the Components of the Push-out Space with Certain Indices
Yusuf
Kaya
Bülent Ecevit University, ZONGULDAK, TURKEY
Given an immersion of a connected, $m$-dimensional manifold $M$ without boundary into the Euclidean $(m+k)$-dimensional space, the idea of the push-out space of the immersion under the assumption that immersion has flat normal bundle is introduced in [3]. It is known that the push-out space has finitely many path-connected components and each path-connected component can be assigned an integer called the index of the component. In this study, when $M$ is compact, we give some new results on the push-out space. Especially it is proved that if the push-out space has a component with index $1$, then the Euler number of $M$ is $0$ and if the immersion has a co-dimension $2$, then the number of path connected components of the push-out space with index $(m-1)$ is at most 2.
General
1
16
10.4171/RSMUP/127-1
http://www.ems-ph.org/doi/10.4171/RSMUP/127-1
The Arithmetic Theory of Local Constants for Abelian Varieties
Marco Adamo
Seveso
Università degli Studi di Milano, MILANO, ITALY
We present a generalization of the theory of local constant developed by B. Mazur and K. Rubin in order to cover the case of abelian varieties, with emphasis to abelian varieties with real multiplication. Let $l$ be an odd rational prime and let $L/K$ be an abelian $l$-power extension. Assume that we are given a quadratic extension $K/k$ such that $L/k$ is a dihedral extension and the abelian variety $A/k$ is defined over $k$ and polarizable. This theory can be used to relate the rank of the $l$-Selmer group of $A$ over $K$ to the rank of the $l$-Selmer group of $A$ over $L$.
General
17
39
10.4171/RSMUP/127-2
http://www.ems-ph.org/doi/10.4171/RSMUP/127-2
Brownian Motion, Reflection Groups and Tanaka Formula
Nizar
Demni
Université de Rennes I, RENNES CEDEX, FRANCE
Dominique
Lépingle
Université d'Orléans, ORLÉANS CEDEX 2, FRANCE
In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka's formula for linear Brownian motion. The paper is closed with a description of the boundary process through the local times of the distances from the initial process to the facets.
General
41
55
10.4171/RSMUP/127-3
http://www.ems-ph.org/doi/10.4171/RSMUP/127-3
Functional Solutions for a Plane Problem in Magnetohydrodinamics
Giovanni
Cimatti
Università di Pisa, PISA, ITALY
We study the flow in a channel of a fluid obeying the equations of magnetohydrodynamics under the hypotheses that viscosity, resistivity and thermal conductivity depend on the temperature. The special class of solutions for which two functional dependences between temperature and magnetic field and velocity and magnetic field exist is considered.
General
57
74
10.4171/RSMUP/127-4
http://www.ems-ph.org/doi/10.4171/RSMUP/127-4
Opérateurs invariants sur un immeuble affine de type $\tilde B_n (n\ge3)$
Ferdaous
Kellil
ISIMM, Université de Monastir, MONASTIR, TUNISIA
Guy
Rousseau
Université de Lorraine, CNRS, VANDOEUVRE LÈS NANCY, FRANCE
We consider a building $\Delta$ of type $\widetilde{B}_n~(n\geq 3)$, different subsets $\mathcal{S}'$ of the set $\mathcal{S}$ of vertices in $\Delta$ and an automorphism group $G$ strongly transitive and type preserving on $\Delta$. We prove that the algebra of $G$-invariant operators acting on the space of functions on $\mathcal{S}'$ is not commutative (contrarily to the classical results) and we give its generators. We give also the precise structure of some commutative subalgebras.
General
75
98
10.4171/RSMUP/127-5
http://www.ems-ph.org/doi/10.4171/RSMUP/127-5
Another Look at Connections
Florin
Dumitrescu
Romanian Academy, BUCHAREST, ROMANIA
In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [F. Dumitrescu, Journal of Homotopy and Related Structures, vol 5, no 1 (2010)] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new approach to connections on a bundle as a consistent way to lift the dynamics of the manifold to the bundle.
General
99
105
10.4171/RSMUP/127-6
http://www.ems-ph.org/doi/10.4171/RSMUP/127-6
Generalized Cotorsion Locally Compact Abelian Groups
N.I.
Kryuchkov
Ryazan State University, RYAZAN, RUSSIAN FEDERATION
This paper is concerned with the generalization of the concept of cotorsion abelian group. A locally compact abelian group $L$ is called generalized cotorsion if $L$ contains a compact open subgroup $K$ such that the character group of $K$ and the group $L/K$ are cotorsion groups. Some properties and homological characteristics of generalized cotorsion groups are obtained. The classification problem of generalized cotorsion groups is discussed.
General
107
120
10.4171/RSMUP/127-7
http://www.ems-ph.org/doi/10.4171/RSMUP/127-7
$\mathscr{A}$-Schemes and Zariski-Riemann Spaces
Satoshi
Takagi
Osaka City University, OSAKA, JAPAN
In this paper, we will investigate further properties of $\mathscr{A}$-schemes introduced in [Tak]. The category of $\mathscr{A}$-schemes possesses many properties of the category of coherent schemes, and in addition, it is co-complete and complete. There is the universal compactification, namely, the Zariski-Riemann space in the category of $\mathscr{A}$-schemes. We compare it with the classical Zariski-Riemann space, and characterize the latter by a left adjoint.
General
121
177
10.4171/RSMUP/127-8
http://www.ems-ph.org/doi/10.4171/RSMUP/127-8
Riccati Differential Equation for Hypergeometric Differential Equation
Takahiro
Nakagawa
Chiba University, CHIBA, JAPAN
In this paper, we study the solutions of Riccati differential equation corresponding to $p$-adic differential equations which are solvable on the generic disc. As an application, we consider the Grothendieck conjecture for Riccati differential equations. We see that the Riccati differential equations for some globally nilpotent differential equation with coefficients in $\mathbb{Q}(t)$ have, for almost all prime, a solution in rational function field over the finite field $\mathbb{F}_p$, but do not have any algebraic solutions.
General
179
192
10.4171/RSMUP/127-9
http://www.ems-ph.org/doi/10.4171/RSMUP/127-9
The Behaviour of Rigid Analytic Functions around Orbits of Elements of $\mathbb{C}_p$
S.
Achimescu
Romanian Academy, BUCHAREST, ROMANIA
V.
Alexandru
University of Bucharest, BUCHAREST, ROMANIA
Nicolae
Popescu
Romanian Academy, BUCHAREST, ROMANIA
Marian
Vâjâitu
Romanian Academy, BUCHAREST, ROMANIA
Alexandru
Zaharescu
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Given a prime number $p$ and the Galois orbit $O(x)$ of an element $x$ of $\mathbb{C}_p$, the topological completion of the algebraic closure of the field of $p$-adic numbers, we study the behavior of rigid analytic functions around orbits of elements of $\mathbb{C}_p$.
General
193
211
10.4171/RSMUP/127-10
http://www.ems-ph.org/doi/10.4171/RSMUP/127-10
Inertial Automorphisms of an Abelian Group
Ulderico
Dardano
Università degli Studi di Napoli Federico II, NAPOLI, ITALY
Silvana
Rinauro
Università degli Studi della Basilicata, POTENZA, ITALY
An automorphisms $\gamma$ of a group is inertial if $X\cap X^\gamma$ has finite index in both $X$ and $X^\gamma$ for any subgroup $X$. We study inertial automorphisms of abelian groups and give characterization of them. In particular, if the group is periodic they have property that $X^{\langle\gamma\rangle}/X_{\langle\gamma\rangle}$ is bounded. We also study finitely generated groups of inertial automorphisms.
General
213
233
10.4171/RSMUP/127-11
http://www.ems-ph.org/doi/10.4171/RSMUP/127-11
A Convergence Theorem for Immersions with $L^2$-Bounded Second Fundamental Form
Cheikh Birahim
Ndiaye
Universität Tübingen, TÜBINGEN, GERMANY
Reiner
Schätzle
Universität Tübingen, TÜBINGEN, GERMANY
In this short note, we prove a convergence theorem for sequences of immersions from some closed surface $\Sigma$ into some standard Euclidean space $\mathbb{R}^n$ with $L^2$-bounded second fundamental form, which is suitable for the variational analysis of the famous Willmore functional, where $n\geq 3$. More precisely, under some assumptions which are automatically verified (up to subsequence and an appropriate Möbius transformation of $\mathbb{R}^n$) by sequences of immersions from some closed surface $\Sigma$ into some standard Euclidean space $\mathbb{R}^n$ arising from an appropriate stereographic projection of $\mathbb{S}^n$ into $\mathbb{R}^n$ of immersions from $\Sigma$ into $\mathbb{S}^n$ and minimizing the $L^2$-norm of the second fundamental form with $n\geq 3$, we show that the varifolds limit of the image of the measures induced by the sequence of immersions is also an immersion with some minimizing properties.
General
235
247
10.4171/RSMUP/127-12
http://www.ems-ph.org/doi/10.4171/RSMUP/127-12
On the Fixed-Point Set and Commutator Subgroup of an Authomorphism of a Group of Finite Rank
B.A.F.
Wehrfritz
Queen Mary University of London, LONDON, UNITED KINGDOM
Let $\phi$ be an automorphism of a group $G$. For $G$ polycyclic, Endimioni and Moravec in [1] discuss the relationship between the fixed-point set $C_G(\phi)$ and the commutator subgroup $[G,\phi]$ of $\phi$ in $G$. Here we extend these results to soluble groups satisfying various rank restrictions.
General
249
255
10.4171/RSMUP/127-13
http://www.ems-ph.org/doi/10.4171/RSMUP/127-13