Pure motives with representable Chow groups

Extensions of motives and higher Chow groups

Bloch’s Conjecture and Chow Motives

Let X be a connected smooth projective complex surface. J. Murre [7] constructed a decomposition of Chow motives for X , i.e. there exist mutually orthogonal idempotents πi ∈ CH (X × X)Q as correspondences for 0 ≤ i ≤ 4 such that ∑ i πi is equal to the diagonal and the action of πi on H (X,Q) is the identity for i = j, and vanishes otherwise. The decomposition is not uniquely characterized by t...

Motives and Chow Groups of Quadrics with Application to the U-invariant (after Oleg Izhboldin)

Numbers Representable in Pure QSIM

The standard number representation for qualitative reasoning is shown to be more powerful than commonly thought. We prove that this scheme, based on ordered lists of symbols for critical values and corresponding value tuples fixing points on the curves relating variables, is sufficient for representing the equality of a landmark to any specified number in the radical extension of the set of rat...

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...