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Relative Equivariant Motives and Modules

Part of: Cycles and subschemes (Co)homology theory Representation theory of groups Special varieties

Published online by Cambridge University Press:  08 November 2019

Baptiste Calmès ,
Alexander Neshitov  and
Kirill Zainoulline
Baptiste Calmès
Affiliation:
Faculté des Sciences Jean Perrin, Université d’Artois, Rue Jean Souvraz SP 18, 62307Lens Cedex, France Email: baptiste.calmes@math.cnrs.fr
Alexander Neshitov
Affiliation:
Department of Mathematics, Western University, Middlesex College, LondonON N6A 5B7 Email: aneshito@uwo.ca
Kirill Zainoulline
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur, OttawaON K1N 6N5 Email: kirill@uottawa.ca
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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.

Keywords

linear algebraic grouptorsorflag varietyequivariant oriented cohomologymotivic decompositionHecke algebra

MSC classification

Primary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds 20C08: Hecke algebras and their representations 14C15: (Equivariant) Chow groups and rings; motives
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 1 , February 2021 , pp. 131 - 159
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

Author B. C. acknowledges the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-12-BL01-0005. Authors A. N. and K. Z. were partially supported by NSERC Discovery Grants.

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