Bruno Kahn: On ``horizontal" invariants attached to quadratic forms

Submission: 2004, Sep 10

This is the TeX-ing of a manuscript from 1993 entitled "Quadratic forms and simple algebras of exponent two". It has been slightly edited. It contains the definition of invariants such the dimension of a quadratic form modulo I^{n+1} (a notion that has recently been succesfully exploited by Vishik), the length of an element in I^n/I^{n+1} and their "global" counterparts: the u-invariant modulo I^{n+1} and the n-th lambda-invariant of a field of characteristic not 2. Some inequalities between these invariants are established, some elementary and some less elementary. Everything is anterior to Voevodsky's proof of the Milnor conjecture, which is not used.

2000 Mathematics Subject Classification: Primary: 11E04, 11E81

Keywords and Phrases: Quadratic forms, dimension, u-invariant

Full text: dvi.gz 23 k, dvi 52 k, ps.gz 638 k, pdf.gz 137 k, pdf 158 k.

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