### An invariant of quadratic forms over schemes, by Marek Szyjewski

A ring homomorphism e^0: W(X)--> EX from the Witt ring of a scheme X into
proper subquotient EX of the Grothendieck ring K_0(X) is a natural
generalisation of dimension index for Witt ring of a field. In the case of
even dimensional projective quadric X over a field F the value of e^0 on the
Witt class of bundle of endomorphisms E of an indecomposable component V_0 of
the Swan sheaf U with trace of product as a bilinear form \theta is outside
of the image of composition W(F)--> W(X)--> E(X). Therefore the Witt class of
(E,\theta) is not extended from F.

This paper has appeared as paper 19 in Documenta
Mathematica, volume 1.

Marek Szyjewski <szyjewski@gate.math.us.edu.pl>

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