Algebraic oriented cohomology theories, by Alexander Merkurjev

For every smooth projective variety over an infinite field F we define its fundamental polynomial in Z[b_1,b_2,...] and prove that the fundamental polynomials generate the Lazard ring Laz in Z[b_1,b_2,...]. Using description of invariant prime ideals in Laz, due to Landweber, we assign to every smooth projective variety X the numbers n_p(X) for every prime integer p. Inequality n_p(Y)>n_p(X) for some prime p is an obstruction for existence of a morphism from Y to X over F.

Alexander Merkurjev <>