### Algebraic Morava K-theories and the higher degree formula, by Simone Borghesi

[This an updated version containing a correction in the statement of
Theorem 4.1.]

The first part of the paper contains the construction of a version of
the algebraic Morava K-theories at a prime q in the stable homotopy
category of schemes over a base field of characteristic 0. They came
equipped with an H_{Z/q}-resolution.

In the second part, we use this construction to prove for a morphism f
a "higher degree formula" t(Y)=deg(f)t(X) mod I(X) relating the degree
of a morhism f:Y->X with certain characteristic numbers of X and Y. We end
the paper by including a result due to M. Rost which gives sufficient
conditions on X for I(X) to vanish. Products of certain norm
varieties are known to satisfy this condition and to have nontrivial
numbers t(X).

Simone Borghesi <simone@math.nwu.edu>