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Hermitian K-theory and 2-regularity for totally real number fields
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In this paper, the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in real 2-regular number fields were determined.Abstract:
We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8. In both the orthogonal and symplectic cases, we prove the 2-primary hermitian Quillen-Lichtenbaum conjecture.read more
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The Homotopy Fixed Point Theorem and the Quillen–Lichtenbaum conjecture in Hermitian K-theory
TL;DR: In this paper, it was shown that the comparison map from the Hermitian K-theory of X to the homotopy fixed points of Ktheory under the natural Z/2 -action is a 2-adic equivalence.
Journal ArticleDOI
Preorientations of the derived motivic multiplicative group
TL;DR: In this article, the authors provide a proof in the language of model categories and symmetric spectra of Lurie's theorem that topological complex $K$-theory represents orientations of the derived multiplicative group.
Journal ArticleDOI
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.
Journal ArticleDOI
Hermitian $K$-theory, Dedekind $\zeta$-functions, and quadratic forms over rings of integers in number fields
TL;DR: In this article, the authors employ the slice spectral sequence, motivic Steenrod algebra, and Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the hermitian $K$-groups of rings of integers in number fields.
References
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TL;DR: In this article, the structure of semisimplepleasure Lie groups and Lie algebras is studied. But the classification of simple Lie algesbras and of symmetric spaces is left open.
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A. K. Bousfield,Daniel M. Kan +1 more
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TL;DR: In this article, the authors define a classfield theory for algebraic number-fields with respect to simple algebras over A-fields and the Brauer group of a local field.
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Symmetric bilinear forms
John Milnor,Dale Husemoller +1 more
TL;DR: In this article, the Hasse-Minkowski Theorem and the Signature mod 8 of the Quadratic Reciprocity Theorem are used to describe the inner product spaces over a field.
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K-theory: An introduction
TL;DR: In this article, the first notion of k-theory and its application in vector bundles are discussed. But they focus on the first notations of K-Theory.