Steenrod operations on the Chow ring of a classifying space

Mathematics – Algebraic Geometry

Scientific paper

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32 pages, uses elsart.cls, submitted to Adv. Math

Scientific paper

We use the Steenrod algebra to study $CH^*BG$, the mod $p$ Chow ring of the classifying space of $G$. We describe a localization property which relates a given $G$ to its elementary abelian subgroups, and we study a number of particular cases, namely symmetric groups and Chevalley groups. It turns out that the Chow rings of these groups are completely determined by the abelian subgroups and their fusion.

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