Baptiste Calmès

A coproduct structure on the formal affine Demazure algebra

In the present paper, we generalize the coproduct structure on nil Hecke rings introduced and studied by Kostant and Kumar to the context of an arbitrary algebraic oriented cohomology theory and its associated formal group law. We then construct an algebraic model of the T-equivariant oriented cohomology of the variety of complete flags.

Push-pull operators on the formal affine Demazure algebra and its dual

In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the dual of the formal affine Demazure algebra which serves as an algebraic counterpart of the natural pairing on the equivariant oriented cohomology of the complete flag variety induced by multiplication and push-forward to a point.

Chow motives of twisted flag varieties

Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of an anisotropic projective G-homogeneous variety in terms of motives of simpler Ghomogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB2(A) of a division algebra A of degree 5 into a direct sum of twisted motives of the Severi-Brauer variety SB(B) of a division algebra B Brauer-equivalent to the tensor square A⊗2. As an application we provide another counter-example to the uniqueness of a direct sum decomposition in the category of motives with integral coefficients. MSC2000: 57T15,19E15

Trivial Witt groups of flag varieties

Abstract Let G be a split semi-simple linear algebraic group over a field k of characteristic not 2 . Let P be a parabolic subgroup and let L be a line bundle on the projective homogeneous variety G / P . We give a simple condition on the class of L in Pic ( G / P ) / 2 in terms of Dynkin diagrams implying that the Witt groups W i ( G / P , L ) are zero for all integers i . In particular, if B is a Borel subgroup, then W i ( G / B , L ) is zero unless L is trivial in Pic ( G / B ) / 2 .