Witt equivalence of fields: A survey with a special emphasis on applications of hyperfields
Author:
- 1 January 2017
- book chapter
- Published by American Mathematical Society (AMS)
- Vol. 697, 169-185
Abstract
Two fields are Witt equivalent if their Witt rings of symmetric bilinear forms are isomorphic. Witt equivalent fields can be understood to be fields having the same quadratic form theory. In this survey we recall old and new results on Witt equivalence of fields. Where applicable, we make extensive use of the notion of hyperfields, which appear to provide a convenient language to study the discusses theory. We provide some short and, to the best of author’s knowledge, new proofs of a few known results, and try to illustrate the theory with numerous examples.Keywords
This publication has 52 references indexed in Scilit:
- Universal Thickening of the Field of Real Numbers2015
- Higher degree tame hilbert-symbol equivalence of number fieldsAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1999
- Higher Degree Hilbert Symbol Equivalence of Algebraic Number Fields, IIJournal of Number Theory, 1998
- Constructible Sets in Real Geometry1996
- Finiteness theorems for forms over global fieldsMathematische Zeitschrift, 1992
- Realizing dyadic factors of elementary type Witt rings and pro-2 Galois groupsMathematische Zeitschrift, 1991
- Fields with prescribed quadratic form schemesMathematische Zeitschrift, 1979
- Quadratic forms over formally real fields with eight square classesmanuscripta mathematica, 1979
- Symmetric Bilinear Forms1973
- Beweis des Krullschen Durchschnittsatzes f r den WittringInventiones Mathematicae, 1971