Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668757 | Bulletin des Sciences Mathématiques | 2015 | 23 Pages |
Abstract
Let F be a field of characteristic 2, and T(F) the set of totally singular F-quadratic forms up to isometry. The uË-invariant of F is the maximal dimension of an anisotropic F-quadratic form. In this paper we introduce new invariants of F related to the uË-invariant. The first one, called uË-invariant, is the maximal dimension of an anisotropic not totally singular F-quadratic form. The motivation of introducing this invariant is to see how the values of the uË-invariant can be given without the use of forms of T(F), this is because most of the known values of the uË-invariant are realized by the forms of T(F) (see [12]). Also, for r,sâ¥1 integers, we introduce the ur-invariant (resp. the uËs-invariant) which is the maximal dimension of an anisotropic F-quadratic form having a regular part of dimension 2r (resp. the maximal dimension of an anisotropic not totally singular F-quadratic form having a quasilinear part of dimension s). We make a comparison between these new invariants by relating them to the u-invariant and the uË-invariant, and we give a list of values that they can take. We also discuss the classical question, due to Baeza [3], on the universality of some nonsingular F-quadratic forms when F has finite u-invariant.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Ahmed Laghribi,