Applications of Atiyah-Hirzebruch spectral sequences for motivic cobordisms, by Nobuaki Yagita

In this paper, we study appications of Atiyah-Hirzebruch spectral sequences for motivic cobordisms recently found by Hopkins and Morel. For example, we compute the mod 2 motivic cohomology of reduced Cech complex of a splitting variety according to Orlov, Vishik and Voevodsky. The cobordism ring MGL/2^{*,*}(Spec(R)) is computed comparing the results of the real cobordism theory by Hu and Kriz. Moreover, we study algebraic cobordims of classifying spaces BG for algebraic groups over C. For example, the Chow ring CH^*(BG_2)_(2) for the exceptional Lie group G_2 is determined by using motivic cobordisms and motivic cohomology.


Nobuaki Yagita <yagita@mx.ibaraki.ac.jp>