2010/07/07 by Amalendu Krishna, Krishna, Amalendu
Mathematics · #14C25 #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14C25 #msc:19E15
paper · pdf · doi:10.48550/arxiv.1007.1083
arxiv created 2010/07/07 · openalex publication_date 2010/07/07 · arxiv updated 2010/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected linear algebraic group over a field k of characteristic zero. For a principal G-bundle π: E → X over a scheme X of finite type over k and a parabolic subgroup P of G, we describe the rational algebraic cobordism and higher Chow groups of the flag bundle E/P → X in terms of the cobordism of X and that of the classifying space of a maximal torus of G contained in P. As a consequence, we also obtain the formula for the cobordism and higher Chow groups of the principal bundles over the scheme X. If X is smooth, this describes the cobordism ring of these bundles in terms of the cobordism ring of X.