CHERN CLASSES FROM MORAVA K-THEORIES TO P N PN upper P Superscript upper N-TYPICAL ORIENTED THEORIES

We study non-additive operations from algebraic Morava K-theories to oriented cohomology theories in algebraic geometry. For oriented cohomology theory A A upper A that has a p n pⁿ p Superscript n -typical formal group law over a Z ( p ) Z₍ₚ₎ double struck upper Z Subscript left parenthesis p right parenthesis -algebra we construct ‘Chern classes’ from the algebraic n n n -th Morava K-theory with p p p -local coefficients to A A upper A . If the coefficient ring of A A upper A is a free Z ( p ) Z₍ₚ₎ double struck upper Z Subscript left parenthesis p right parenthesis -module we also prove that these Chern classes freely generate all operations from