Two-primary algebraic K-theory of two-regular number fields
John Rognes,Paul Arne Østvær +1 more
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In this article, the 2-primary higher algebraic K-groups of the rings of integers of all 2-regular quadratic number fields, cyclotomic number fields or maximal real subfields of such are explicitly calculated.Abstract:
We explicitly calculate all the 2-primary higher algebraic K-groups of the rings of integers of all 2-regular quadratic number fields, cyclotomic number fields, or maximal real subfields of such. Here 2-regular means that (2) does not split in the number field, and its narrow Picard group is of odd order.read more
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Book
The K-Book: An Introduction to Algebraic K-theory
TL;DR: Projective modules and vector bundles The Grothendieck group $K 0$ $K 1$ and $K 2$ of a ring Definitions of higher $K$-theory The fundamental theorems of higher$K$theory as mentioned in this paper.
Journal ArticleDOI
Two-primary algebraic k-theory of rings of integers in number fields
TL;DR: In this article, the two-primary K-theory of a totally real number field F and its ring of integers was shown to converge to its étale cohomology when F is Abelian.
Algebraic K-Theory of Rings of Integers in Local and Global Fields
TL;DR: The problem of computing the higher K-theory of a number field F, and of its rings of integers OF, has a rich history as mentioned in this paper, and the resolutions of many of these conjectures by Suslin, Voevodsky, Rost and others have finally made it possible to describe the groups K∗(OF ).
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Periodicity of hermitian K -groups
TL;DR: In this article, it was shown that the periodicity of the algebraic K-groups for any ring implies periodicity for the hermitian K-group, analogous to orthogonal and symplectic topological K-theory.
Book ChapterDOI
The Homotopy Type of Two-regular K-theory
Luke Hodgkin,Paul Arne Østvær +1 more
TL;DR: In this paper, the authors identify the 2-adic homotopy type of the algebraic K-theory space for rings of integers in two-regular exceptional number fields, in terms of well-known spaces considered in topological Ktheory.
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