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.

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.

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.

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.

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

The (α, β)-ramification invariants of a number field

2021 ◽  
Vol 71 (1) ◽  
pp. 251-263
Author(s):  
Guillermo Mantilla-Soler
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Residue Class ◽  
Interesting Application ◽  
Dedekind Zeta Function ◽  
Arithmetic Properties

Abstract Let L be a number field. For a given prime p, we define integers α p L $ \alpha_{p}^{L} $ and β p L $ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, β p L $ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and α p L $ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of α p L $ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.

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