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Kirill Zainoulline

Bio: Kirill Zainoulline is an academic researcher from University of Ottawa. The author has contributed to research in topics: Cohomology & Linear algebraic group. The author has an hindex of 15, co-authored 80 publications receiving 814 citations. Previous affiliations of Kirill Zainoulline include University of Alberta & Bielefeld University.


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TL;DR: In this paper, the authors introduce le J-invariant de G which caracterises le comportement motivique de X and generalise le J invariant defini par A. Vishik dans le cadre des formes quadratiques.
Abstract: Soit G un groupe algebrique lineaire semi-simple de type interieur sur un corps F et soit X un G-espace homogene projectif tel que le groupe G soit deploye sur le point generique de X. Nous introduisons le J-invariant de G qui caracterise le comportement motivique de X et generalise le J-invariant defini par A. Vishik dans le cadre des formes quadratiques. Nous utilisons cet invariant pour obtenir les decompositions motiviques de tous les G-espaces homogenes projectifs qui sont generiquement deployes, par exemple les varietes de Severi-Brauer, les quadriques de Pfister, la grassmannienne des sous-espaces totalement isotropes maximaux d'une forme quadratique, la variete des sous-groupes de Borel de G. Nous discutons egalement les relations avec les indices de torsion, la dimension canonique et les invariants cohomologiques du groupe G.

97 citations

Posted Content
TL;DR: In this article, the authors generalize the classical work of Demazure [Invariants symetriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws.
Abstract: In the present notes we generalize the classical work of Demazure [Invariants symetriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple linear algebraic group over a field and let T be its split maximal torus. We construct a generalized characteristic map relating the so called formal group ring of the character group of T with the cohomology of the variety of Borel subgroups of G. The main result of the paper says that the kernel of this map is generated by W-invariant elements, where W is the Weyl group of G. As one of the applications we provide an algorithm (realized as a Macaulau2 package) which can be used to compute the ring structure of an oriented cohomology (algebraic cobordism, Morava $K$-theories, connective K-theory, Chow groups, K_0, etc.) of a complete flag variety.

51 citations

Journal ArticleDOI
TL;DR: For an oriented cohomology theory A and a relative cellular space X, the authors decompose the A -motive of X into a direct sum of twisted motives of the base spaces.

48 citations

Journal ArticleDOI
TL;DR: In this paper, the authors generalize the classical work of Demazure [Invariants symetriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws.
Abstract: In the present notes we generalize the classical work of Demazure [Invariants symetriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple linear algebraic group over a field and let T be its split maximal torus. We construct a generalized characteristic map relating the so called formal group ring of the character group of T with the cohomology of the variety of Borel subgroups of G. The main result of the paper says that the kernel of this map is generated by W-invariant elements, where W is the Weyl group of G. As one of the applications we provide an algorithm (realized as a Macaulau2 package) which can be used to compute the ring structure of an oriented cohomology (algebraic cobordism, Morava $K$-theories, connective K-theory, Chow groups, K_0, etc.) of a complete flag variety.

45 citations

Journal ArticleDOI
TL;DR: In this paper, the authors generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0, connective K-theory, elliptic cohomologies, and algebraic cobordism.
Abstract: In the present paper we generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings respectively. We also introduce a deformed version of the formal (affine) Demazure algebra, which we call a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.

38 citations


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01 Jan 2016
TL;DR: The reflection groups and coxeter groups is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you for downloading reflection groups and coxeter groups. Maybe you have knowledge that, people have search numerous times for their favorite books like this reflection groups and coxeter groups, but end up in malicious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they cope with some infectious bugs inside their computer. reflection groups and coxeter groups is available in our digital library an online access to it is set as public so you can download it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the reflection groups and coxeter groups is universally compatible with any devices to read.

450 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce le J-invariant de G which caracterises le comportement motivique de X and generalise le J invariant defini par A. Vishik dans le cadre des formes quadratiques.
Abstract: Soit G un groupe algebrique lineaire semi-simple de type interieur sur un corps F et soit X un G-espace homogene projectif tel que le groupe G soit deploye sur le point generique de X. Nous introduisons le J-invariant de G qui caracterise le comportement motivique de X et generalise le J-invariant defini par A. Vishik dans le cadre des formes quadratiques. Nous utilisons cet invariant pour obtenir les decompositions motiviques de tous les G-espaces homogenes projectifs qui sont generiquement deployes, par exemple les varietes de Severi-Brauer, les quadriques de Pfister, la grassmannienne des sous-espaces totalement isotropes maximaux d'une forme quadratique, la variete des sous-groupes de Borel de G. Nous discutons egalement les relations avec les indices de torsion, la dimension canonique et les invariants cohomologiques du groupe G.

97 citations