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Isomorphism criteria for Witt rings of real fields
-
Nicolas Grenier-Boley
,
Detlev W. Hoffmann
Published/Copyright:
January 3, 2013
Abstract.
We prove isomorphism criteria for Witt rings and reduced Witt rings of certain types of real fields. Refined criteria are obtained under the additional assumption that the field be SAP. This leads to a generalization of a result by Koprowski on Witt equivalence of function fields of transcendence degree 1 over a real closed field. Isomorphism criteria are also obtained for Witt rings of hermitian forms over a quadratic extension of a real base field and for Witt groups of hermitian forms over a quaternion algebra with a real field as center. All these criteria are expressed in terms of properties involving topological subspaces of the space of orderings of the base field.
Keywords: Witt ring; reduced Witt ring; Witt group; real
field; ordering; preordering; Witt equivalence; hermitian form; quadratic form; quaternion algebra; function field
Received: 2010-05-25
Published Online: 2013-01-03
Published in Print: 2013-01-01
© 2013 by Walter de Gruyter Berlin Boston
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- Isomorphism criteria for Witt rings of real fields
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- Cofiniteness of composed local cohomology modules
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Keywords for this article
Witt ring;
reduced Witt ring;
Witt group;
real
field;
ordering;
preordering;
Witt equivalence;
hermitian form;
quadratic form;
quaternion algebra;
function field
Articles in the same Issue
- Masthead
- Isomorphism criteria for Witt rings of real fields
- Simplicial differential calculus, divided differences, and construction of Weil functors
- Rank 3 permutation characters and maximal subgroups
- On the oscillation and nonoscillation of the solutions of impulsive differential equations of second order with retarded argument
- A note on the existence of transition probability densities of Lévy processes
- Carleson measures and Logvinenko–Sereda sets on compact manifolds
- Cofiniteness of composed local cohomology modules
- Real hypersurfaces of type (A) in complex two-plane Grassmannians related to the commuting shape operator
- Deconstructibility and the Hill Lemma in Grothendieck categories
