Classifying spaces, steenrod operations and algebraic closure
نویسندگان
چکیده
منابع مشابه
Steenrod operations on the Chow ring of a classifying space
We use the Steenrod algebra to study the Chow ring CH∗BG of the classifying space of an algebraic group 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 ...
متن کاملExtended Powers and Steenrod Operations in Algebraic Geometry
Steenrod operations were defined by Voedvodsky in motivic cohomology in order to prove the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings [5]. The purpose of this paper is to provide a setting for the construction of the Steenrod operations in algebraic geometry, for generalized cohomology theories whose formal group law has order two. W...
متن کاملAlgebraic Cobordism of Classifying Spaces
We define algebraic cobordism of classifying spaces, Ω∗(BG) and G-equivariant algebraic cobordism Ω∗G(−) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F (Ω(−)), which are required for the definition to work. We show that G-equivariant cobordism satisfies the localization exact sequence. We calculate Ω(BG) for algebraic groups...
متن کاملSecondary Steenrod Operations in Cohomology of Infinite-Dimensional Projective Spaces
The important role of the Steenrod operations Sq in the description of the cohomology of topological spaces, the calculation of various spectral sequences, and the study of homotopy properties of topological spaces and their continuous maps is well known [1, 2]. Projective spaces, in particular RP∞ and CP∞ , play a special role in the construction of Steenrod operations and their computation. I...
متن کاملSteenrod operations on Schubert classes
Let G be a compact connected Lie group andH the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan
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ژورنال
عنوان ژورنال: Topology
سال: 1977
ISSN: 0040-9383
DOI: 10.1016/0040-9383(77)90003-9