by Markus Rost (Preprint, March 99, 17 pages)
With corrections/additions of May/June 2006
For i = 6, 7 we define invariants hi:
H1(k,Spin14) -> Hi(k,Z/2) (if -1
is a square).
Further we show that the natural map H1(k,H) ->
H1(k,Spin14) is surjective, where H is the
normalizer of G2×G2 in
Spin14.
One concludes that the essential dimension of Spin14 is
equal to 7.
Similar considerations are done for Spin12.
For Spin13 we use the results about Spin14 and some
special computations.
We present the list of essential dimensions of the split groups
Spinn for n less or equal to 14.
See also: Cohomological invariants, by Skip Garibaldi, June 2006
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by Markus Rost (Preprint, May 94, 5 pages)
The isotropy group of a 14-dimensional spinor is G2×G2. This fact has the following consequence:
A 14-dimensional quadratic form with trivial discriminant and trivial Hasse-Witt invariant is isomorphic to the trace of the pure subform of a 3-fold Pfister form (times a trace zero element) over some quadratic extension.
The text originates from an email in May 1994. It has been revised on September 18, 1996 and March 9, 1999 (but still may contain some inaccuracies).
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