2016/09/30 by Baptiste Calmès, Alexander Neshitov, Kirill Zainoulline
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cohomology #Context (archaeology) #Flag (linear algebra) #Indecomposable module #Mathematical proof #Type (biology) #Variety (cybernetics) #math.AG #math.RT #msc:14C15 #msc:14F43 #msc:14M15 #msc:20C08
paper · pdf · doi:10.4153/s0008414x19000543
published as Can. J. Math.-J. Can. Math. 73 (2021) 131-159 · 25pp; This is a substantially revised and reorganized version. Several proofs were revised and simplified. Examples added
openalex created_date 2018/04/13 · arxiv created 2019/06/25 · openalex publication_date 2019/11/08 · arxiv updated 2021/01/20 · openalex updated_date 2026/08/05
Abstract We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag variety depends on the direct sum decomposition type of the parabolic module. To do this we use localization techniques of Kostant and Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties.