Chern classes, K-theory and Landweber exactness over nonregular base schemes

英文摘要：

The purpose of this paper is twofold. First, we use the motivic Landweber exact functor theorem to deduce that the Bott inverted infinite projective space is homotopy algebraic $K$-theory. The argument is considerably shorther than any other known proofs and serves well as an illustration of the effectiveness of Landweber exactness. Second, we dispense with the regularity assumption on the base scheme which is often implicitly required in the notion of oriented motivic ring spectra. The latter allows us to verify the motivic Landweber exact functor theorem and the universal property of the algebraic cobordism spectrum for every noetherian base scheme of finite Krull dimension.