Algebraic cobordism II

For any field k of characteristic 0 we prove for algabraic cobordism the analogue of a theorem of Quillen on complex cobordism: the cobordism ring of the ground field is the Lazard ring L and for any smooth k-variety X, the algebraic cobordism ring Omega*(X) is generated as an L-module, by I is an element of Omega (0)(X) and the element of positive degrees. This implies Rost's conjectured degree formula. We also give a relation between the Chow ring, the K-0 of a smooth k-variety X and Omega*(X). (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.