Cohomological invariants associated to symmetric bilinear forms 
J. F. Jardine

This is a corrected version of a paper that has been published 
(Expositiones Math. 10 (1992), 97-134). 
There is a bad printer error which makes the introduction of the 
published version completely unintelligible. 

Abstract: This paper reviews the construction of the Hasse-Witt 
and Stiefel-Whitney classes for an orthogonal representation of 
a Galois group, and then gives a simplicial presheaf theoretic 
demonstration of the Frohlich-Kahn-Snaith formula for the Hasse-Witt 
invariant of the associated twisted form. A Steenrod squares argument 
is used to show that this formula has an analogue in degree 3. The 
mod 2 \'etale cohomology of the classifying simplicial scheme of the 
automorphism group of an arbitrary non-degenerate symmetric bilinear 
form is calculated, and the relation of this cohomology ring with 
the Hasse-Witt classes of the Frohlich twisted form is discussed. 

This paper was written in LAMSTeX, so the dvi file requires the 
lams* fonts to view or print.