Simplification of λ-ring expressions in the Grothendieck ring of Chow motives

Grothendieck Chow-motives of Severi-Brauer varieties

For any central simple algebra, the Grothendieck Chow-motive of the corresponding Severi-Brauer variety is decomposed in a direct sum where each summand is a twisted motive of the Severi-Brauer variety corresponding to the underlying division algebra. It leads to decompositions in other theories (for instance, of K-cohomologies) because of the universal property of the Chow-motives. In the seco...

The Chow-Witt ring

On the Chow Ring Of

We describe the Chow ring with rational coefficients of the moduli space of stable maps with marked points M0,m(P , d) as the subring of invariants of a ring B(M0,m(P , d);Q), relative to the action of the group of symmetries Sd. B (M0,m(P , d);Q) is computed by following a sequence of intermediate spaces for M0,m(P , d) and relating them to substrata of M0,1(P , d + m − 1). An additive basis f...

Conics in the Grothendieck ring

The Grothendieck ring of k-varieties is still very poorly understood. In characteristic zero, the quotient of K0[Vark] by the ideal generated by [A ] is naturally isomorphic to the ring Z[SBk], where Z[SBk] is the free abelian group generated by the stable birational equivalence classes of smooth, projective, irreducible k-varieties and multiplication is given by the product of varieties [Lar-L...

The Chow Ring of the Cayley Plane

We give a full description of the Chow ring of the complex Cayley plane OP. For this, we describe explicitely the most interesting of its Schubert varieties and compute their intersection products. Translating our results in the Borel presentation, i.e. in terms of Weyl group invariants, we are able to compute the degree of the variety of reductions Y8 introduced in [6].