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6 results on '"19G38"'

1. Algebraic and Homological Aspects of Hermitian -Theory.

Author

Popelensky, Th. Yu.

Abstract

In 1970, S. P. Novikov proposed a systematization of algebraic results of the surgery theory based on the Hamiltonian formalism over rings with involution. His results have had a significant impact on the development of Hermitian analogs of algebraic -theory. This article was written at S. P. Novikov's suggestion and aims to present the current state of research at the interface between the problems of manifold theory and Hermitian -theory of rings with involution. [ABSTRACT FROM AUTHOR]

Published
2024
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3. Stability for odd unitary $K_1$

Author

Voronetsky, Egor

Subjects
Mathematics - Group Theory, 19G38
Abstract

We give a new purely algebraic approach to odd unitary groups using odd form rings. Using these objects, we prove the stability theorems for odd unitary $K_1$-functor without using the corresponding result from linear $K$-theory under the ordinary stable rank condition. Moreover, we prove a natural stabilization result for projective unitary groups and various general unitary groups., Comment: The main result was strengthened

Published
2019
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4. The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes.

Author

Schlichting, Marco

Subjects
*WITT group, *HERMITIAN operators, *K-theory, *ALGEBRAIC fields, *APPROXIMATION theory
Abstract

We prove localization and Zariski-Mayer-Vietoris for higher Gro-thendieck-Witt groups, alias hermitian K-groups, of schemes admitting an ample family of line-bundles. No assumption on the characteristic is needed, and our schemes can be singular. Along the way, we prove Additivity, Fibration and Approximation theorems for the hermitian K-theory of exact categories with weak equivalences and duality. [ABSTRACT FROM AUTHOR]

Published
2010
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5. Stabilization of the Witt group

Author

Max Karoubi

Subjects
19G38, Noetherian, Pure mathematics, Mathematics::Commutative Algebra, Homotopy, K-Theory and Homology (math.KT), General Medicine, Homology (mathematics), Witt group, Mathematics::Algebraic Topology, Category of rings, Mathematics::K-Theory and Homology, Mathematics - K-Theory and Homology, FOS: Mathematics, Torsion (algebra), Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Algebraic number, Topological theory, Mathematics
Abstract

Using an idea due to R.Thomason, we define a "homology theory" on the category of rings which satisfies excision, exactness, homotopy (in the algebraic sense) and periodicity of order 4. For regular noetherian rings, we find P. Balmer's higher Witt groups. For more general rings, this homology isomorphic to the KT-theory of J. Hornbostel, inspired by the work of B. Williams. For real or complex C*-algebras, we recover - up to 2 torsion - topological K-theory., 6 pages ; see also http://www.math.jussieu.fr/~karoubi/

Published
2006
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