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 <>