The weak isotropy of quadratic forms over field extensions

The weak isotropy index (or equivalently, sublevel) of arbitrary quadratic forms is studied. Its relationship to the level of a form is investigated. The problem of determining the set of values of the weak isotropy index of a form as it ranges over field extensions is addressed, with both admissibl...

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Bibliographic Details
Published inManuscripta mathematica Vol. 145; no. 1-2; pp. 143 - 161
Main Author O’Shea, James
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2014
Subjects
Algebraic Geometry
Calculus of Variations and Optimal Control; Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
11E04
11E25
11E10
12D15
11E81
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Summary:The weak isotropy index (or equivalently, sublevel) of arbitrary quadratic forms is studied. Its relationship to the level of a form is investigated. The problem of determining the set of values of the weak isotropy index of a form as it ranges over field extensions is addressed, with both admissible and inadmissible numbers being determined. An analogous investigation with respect to the level of a form is also undertaken. A treatment of forms for which the above invariants coincide concludes this article, with some recently-raised questions being resolved.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-014-0671-0