Groupes et algébres de lie

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/63B506EB85D6875966CE63BA0336BC2F/S0025557200190515a.pdf/div-class-title-span-class-italic-lie-groups-and-lie-algebras-chapters-1-3-span-by-n-bourbaki-pp-450-dm-98-1989-isbn-3-540-50218-1-springer-div.pdf

Lie groups and Lie algebras (chapters 1-3 ), by N. Bourbaki. Pp 450. DM 98. 1989. ISBN 3-540-50218-1 (Springer)

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Reflection Groups And Coxeter Groups

Quadratic and hermitian forms over rings

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.

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J-invariant of linear algebraic groups

We provide a general algorithm used to prove purity for functors with transfers. As a basic example we consider the Witt group of an algebraic variety.

Witt Groups of Varieties and the Purity Problem

We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extending several result and construction (presentation in terms of generators and relations, coproduct and product structures, filtration by codimension of Bott-Samelson classes, root polynomials and multiplication formulas) that were previously known for finite root system.

Formal affine Demazure and Hecke algebras of Kac-Moody root systems

Localized operations on T-equivariant oriented cohomology of projective homogeneous varieties

We apply the degree formula for connective $K$-theory to study rational contractions of algebraic varieties. Examples include rationally connected varieties and complete intersections.

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Degree formula for connective K-theory

In the present paper we extend the theory of sheaves on moment graphs due to Braden-MacPherson and Fiebig to the context of an arbitrary oriented equivariant cohomology $h$ (e.g. to algebraic cobordism). We introduce and investigate structure $h$-sheaves on double moment graphs to describe equivariant oriented cohomology of products of flag varieties. We show that in the case of a total flag variety $X$ the space of global sections of the double structure $h$-sheaf also describes endomorphism ring of the equivariant $h$-motive of $X$.

Kirill Zainoulline

Papers

Witt Groups of Varieties and the Purity Problem

Formal affine Demazure and Hecke algebras of Kac-Moody root systems

Localized operations on T-equivariant oriented cohomology of projective homogeneous varieties

Degree formula for connective K-theory

Oriented sheaves on double moment graphs