For
a field, we construct a power structure on the Grothendieck–Witt ring of
which
has the potential to be compatible with symmetric powers of varieties and the
motivic Euler characteristic. We then show our power structure is compatible
with the variety power structure when we restrict to varieties of dimension
,
using techniques of Garibaldi, Merkurjev and Serre about cohomological
invariants.
Keywords
symmetric powers, motivic homotopy, power structures, Euler
characteristic
