scholarly journals K-Theory of Locally Compact Modules over Rings of Integers

2018 ◽  
Vol 2020 (6) ◽  
pp. 1748-1793 ◽  
Author(s):  
Oliver Braunling
Keyword(s):  
Recent Result ◽  
Number Field ◽  
Independent Interest ◽  
Locally Compact ◽  
Exact Category ◽  
Rings Of Integers ◽  
K Theory ◽  
Special Case

Abstract We generalize a recent result of Clausen; for a number field with integers $\mathcal{O}$, we compute the K-theory of locally compact $\mathcal{O}$-modules. For the rational integers this recovers Clausen’s result as a special case. Our method of proof is quite different; instead of a homotopy coherent cone construction in $\infty$-categories, we rely on calculus of fraction type results in the style of Schlichting. This produces concrete exact category models for certain quotients, a fact that might be of independent interest. As in Clausen’s work, our computation works for all localizing invariants, not just K-theory.

scholarly journals Hermitian periodicity and cohomology of infinite orthogonal groups

2013 ◽  
Vol 12 (1) ◽  
pp. 203-211
Author(s):  
A. J. Berrick ◽  
M. Karoubi ◽  
P. A. Østvær
Keyword(s):  
Number Field ◽  
Symplectic Groups ◽  
Orthogonal Groups ◽  
Rings Of Integers ◽  
K Theory

AbstractAs an application of our papers in hermitian K-theory, in favourable cases we prove the periodicity of hermitian K-groups with a shorter period than previously obtained. We also compute the homology and cohomology with field coeffcients of infinite orthogonal and symplectic groups of specific rings of integers in a number field.

A NOTE ON THE NORMS OF TRANSITION OPERATORS ON LAMPLIGHTER GRAPHS AND GROUPS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1261-1272 ◽  
Author(s):  
WOLFGANG WOESS
Keyword(s):  
Random Walk ◽  
Wreath Products ◽  
Locally Compact Group ◽  
Operator Matrix ◽  
Locally Compact ◽  
Finitely Generated Groups ◽  
Group Of Isometries ◽  
Transition Operators ◽  
Special Case ◽  
Product Of Groups

Let L≀X be a lamplighter graph, i.e., the graph-analogue of a wreath product of groups, and let P be the transition operator (matrix) of a random walk on that structure. We explain how methods developed by Saloff-Coste and the author can be applied for determining the ℓp-norms and spectral radii of P, if one has an amenable (not necessarily discrete or unimodular) locally compact group of isometries that acts transitively on L. This applies, in particular, to wreath products K≀G of finitely-generated groups, where K is amenable. As a special case, this comprises a result of Żuk regarding the ℓ2-spectral radius of symmetric random walks on such groups.

ASYMPTOTICS OF THE WEIGHTED DELANNOY NUMBERS

2012 ◽  
Vol 08 (01) ◽  
pp. 175-188 ◽  
Author(s):  
ROB NOBLE
Keyword(s):  
Number Field ◽  
Asymptotic Expansions ◽  
Lattice Paths ◽  
Delannoy Numbers ◽  
Divisibility Properties ◽  
Special Case

The weighted Delannoy numbers give a weighted count of lattice paths starting at the origin and using only minimal east, north and northeast steps. Full asymptotic expansions exist for various diagonals of the weighted Delannoy numbers. In the particular case of the central weighted Delannoy numbers, certain weights give rise to asymptotic coefficients that lie in a number field. In this paper we apply a generalization of a method of Stoll and Haible to obtain divisibility properties for the asymptotic coefficients in this case. We also provide a similar result for a special case of the diagonal with slope 2.

On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant

2009 ◽  
Vol 16 (4) ◽  
pp. 693-704
Author(s):  
Harun Karsli ◽  
Paulina Pych-Taberska
Keyword(s):  
Recent Result ◽  
Pointwise Convergence ◽  
Rates Of Convergence ◽  
Durrmeyer Operators ◽  
The One ◽  
Special Case ◽  
Appl Math ◽  
Bézier Variant

Abstract We consider the Bézier variant of Chlodovsky–Durrmeyer operators 𝐷𝑛,α for functions 𝑓 measurable and locally bounded on the interval [0,∞). By using the Chanturia modulus of variation we estimate the rate of pointwise convergence of (𝐷𝑛,α 𝑓) (𝑥) at those 𝑥 > 0 at which the one-sided limits 𝑓(𝑥+), 𝑓(𝑥–) exist. In the special case α = 1 the recent result of [Ibikli, Karsli, J. Inequal. Pure Appl. Math. 6: 12, 2005] concerning the Chlodovsky–Durrmeyer operators 𝐷𝑛 is essentially improved and extended to more general classes of functions.

On a Theorem of Kawamoto on Normal Bases of Rings of Integers, II

2005 ◽  
Vol 48 (4) ◽  
pp. 576-579 ◽  
Author(s):  
Humio Ichimura
Keyword(s):  
Prime Number ◽  
Number Field ◽  
Class Group ◽  
Natural Homomorphism ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Integral Basis ◽  
Rings Of Integers ◽  
Integer Ring ◽  
The Ideal

AbstractLet m = pe be a power of a prime number p. We say that a number field F satisfies the property when for any a ∈ F×, the cyclic extension F(ζm, a1/m)/F(ζm) has a normal p-integral basis. We prove that F satisfies if and only if the natural homomorphism is trivial. Here K = F(ζm), and denotes the ideal class group of F with respect to the p-integer ring of F.

scholarly journals A Gap Principle for Subvarieties with Finitely Many Periodic Points

2020 ◽  
Vol 63 (2) ◽  
pp. 382-392
Author(s):  
Keping Huang
Keyword(s):  
Number Field ◽  
Algebraic Variety ◽  
Initial Point ◽  
Periodic Points ◽  
Gap Principle ◽  
Special Case

AbstractLet $f:X\rightarrow X$ be a quasi-finite endomorphism of an algebraic variety $X$ defined over a number field $K$ and fix an initial point $a\in X$. We consider a special case of the Dynamical Mordell–Lang Conjecture, where the subvariety $V$ contains only finitely many periodic points and does not contain any positive-dimensional periodic subvariety. We show that the set $\{n\in \mathbb{Z}_{{\geqslant}0}\mid f^{n}(a)\in V\}$ satisfies a strong gap principle.

scholarly journals The Fourier Algebra for Locally Compact Groupoids

2004 ◽  
Vol 56 (6) ◽  
pp. 1259-1289 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Duality Theorem ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Fourier Algebra ◽  
Hilbert Modules ◽  
Locally Compact ◽  
Classical Duality ◽  
Special Case

AbstractWe introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard.

scholarly journals On groups with locally compact asymptotic cones

2015 ◽  
Vol 25 (01n02) ◽  
pp. 37-40
Author(s):  
Mark Sapir
Keyword(s):  
Group Theory ◽  
Recent Result ◽  
Asymptotic Cone ◽  
Finitely Generated ◽  
Stable Group ◽  
Locally Compact ◽  
Asymptotic Cones ◽  
Finitely Generated Group

We show how a recent result of Hrushovsky [Stable group theory and approximate subgroups, J. Amer. Math. Soc.25(1) (2012) 189–243] implies that if an asymptotic cone of a finitely generated group is locally compact, then the group is virtually nilpotent.

scholarly journals Equivariant KK-theory for generalised actions and Thom isomorphism in groupoid twisted K-theory

2013 ◽  
Vol 13 (1) ◽  
pp. 83-113 ◽  
Author(s):  
El-Kaïoum M. Moutuou
Keyword(s):  
Vector Bundles ◽  
Isomorphism Theorem ◽  
Locally Compact ◽  
Bott Periodicity ◽  
C Algebras ◽  
Thom Isomorphism ◽  
K Theory ◽  
Thom Isomorphism Theorem

AbstractWe develop equivariant KK–theory for locally compact groupoid actions by Morita equivalences on real and complex graded C*-algebras. Functoriality with respect to generalised morphisms and Bott periodicity are discussed. We introduce Stiefel-Whitney classes for real or complex equivariant vector bundles over locally compact groupoids to establish the Thom isomorphism theorem in twisted groupoid K–theory.

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