On reduction maps for the étale and Quillen K-theory of curves and applications

2008 ◽  
Vol 2 (1) ◽  
pp. 103-122 ◽  
Author(s):  
Stefan Barańczuk ◽  
Krzysztof Górnisiewicz
Keyword(s):  
Number Field ◽  
Linear Dependence ◽  
K Theory

AbstractIn this paper we consider reduction of nontorsion elements in the étale and Quillen K-theory of a curve X over a number field. As an application we solve two problems: detecting linear dependence and the support problem.

scholarly journals Diophantine approximation on polynomial curves

2017 ◽  
Vol 163 (3) ◽  
pp. 533-546 ◽  
Author(s):  
JOHANNES SCHLEISCHITZ
Keyword(s):  
Euclidean Space ◽  
Number Field ◽  
Rational Approximation ◽  
Diophantine Approximation ◽  
Rational Number ◽  
Linear Dependence ◽  
Arbitrary Dimension ◽  
Approximation Properties ◽  
Polynomial Curves

AbstractIn a paper from 2010, Budarina, Dickinson and Levesley studied the rational approximation properties of curves parametrised by polynomials with integral coefficients in Euclidean space of arbitrary dimension. Assuming the dimension is at least three and excluding the case of linear dependence of the polynomials together with P(X) ≡ 1 over the rational number field, we establish proper generalisations of their main result.

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 Comparison of Karoubi's regulator and the p-adic Borel regulator

2011 ◽  
Vol 9 (3) ◽  
pp. 579-600 ◽  
Author(s):  
Georg Tamme
Keyword(s):  
Number Field ◽  
K Theory ◽  
Rational Factor

AbstractIn this paper we prove the p-adic analogue of a result of Hamida [11], namely that the p-adic Borel regulator introduced by Huber and Kings for the K-theory of a p-adic number field equals Karoubi's p-adic regulator up to an explicit rational factor.

On a local to global principle in étale K-groups of curves

2013 ◽  
Vol 12 (1) ◽  
pp. 183-201 ◽  
Author(s):  
Grzegorz Banaszak ◽  
Piotr Krasoń
Keyword(s):  
Number Field ◽  
Linear Dependence ◽  
Irreducible Curve ◽  
Almost All ◽  
Global Principle

AbstractLetXbe a smooth, proper and geometrically irreducible curveXdefined over a number fieldFand letχbe a regular and proper model ofXoverOF,Sl. In this paper we address the problem of detecting the linear dependence over ℤlof elements in the étaleK-theory ofχ. To be more specific, letP∊Ket2n(χ)and let ⋀̂ ⊂Ket2n(χ)be a ℤl-submodule. Letrυ:Ket2n(χ)→Ket2n(χυ)be the reduction map for υ ∉Sl. We prove, under some conditions onX, that ifrυ($\(P)_circumflex\$) ∈rυ(⋀̂) for almost all υ of$\mathematical script capital(O) F,Sl\$then$\(P)_circumflex\$∈ ⋀̂ +Ket2n(χ)tor.

On the K-theory of elliptic curves

1999 ◽  
Vol 1999 (507) ◽  
pp. 81-91
Author(s):  
Kevin P Knudson
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Number Field ◽  
Function Field ◽  
Coordinate Ring ◽  
Infinite Field ◽  
Closed Point ◽  
K Theory

Abstract Let A be the coordinate ring of an affine elliptic curve (over an infinite field k) of the form X – {p}, where X is projective and p is a closed point on X. Denote by F the function field of X. We show that the image of H.(GL2 (A), ℤ) in H.(GL2 (F), ℤ) coincides with the image of H.(GL2 (k), ℤ). As a consequence, we obtain numerous results about the K-theory of A and X. For example, if k is a number field, we show that r2 (K2 (A) ⊗ ℚ) = 0, where rm denotes the mth level of the rank filtration.

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.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

K-STRATUM LIMIT AND K-STRATUM INTEGRAL ON THE GENERALIZED NUMBER FIELD

1982 ◽  
Vol 2 (4) ◽  
pp. 375-388
Author(s):  
Jiwu Wang ◽  
Tai Kang
Keyword(s):  
Number Field

On a question of swan in algebraic k-theory

1973 ◽  
Vol 6 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Pramod K. Sharma ◽  
Jan R. Strooker
Keyword(s):  
K Theory
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