### 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 <merkurev@math.ucla.edu>