One of the well-known problem in the algebraic K-theory is the Gersten conjecture. The geometric case of this conjecture was proved by D. Quillen. The equi-characteristic case of the conjecture isâ€¦ (More)

This preprint contains proofs of the results anounced in [PS] in the part concerning the construction of push-forwards for an oriented cohomology theory. It is constructed one-to-one correspondencesâ€¦ (More)

An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P 1-spectra, equipped with the symmetricâ€¦ (More)

It is proved that under certain conditions the group Kn(X) of a smooth projective variety X over a field F is a natural direct summand of Kn(A) for some separable F -algebra. As an application weâ€¦ (More)

A conjecture of F.Morel states that the motivic group Ï€0,0(k) of a perfect field k coincides with the Grothendieck-Witt group GW (k) of quadratic forms over k provided that char(k) 6= 2. Morelâ€™sâ€¦ (More)

The quaternionic Grassmannian HGr(r, n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which theâ€¦ (More)

Notion of an oriented cohomology pretheory on algebraic varieties is introduced and a Riemann-Roch theorem for ring morphisms between oriented pretheories is proved. An explicit formula for the Toddâ€¦ (More)

We prove the Gersten conjecture for Witt groups in the equicharacteristic case, that is for regular local rings containing a field of characteristic not 2.

Let R be a regular local ring, K its field of fractions and (V, Ï†) a quadratic space over R. In the case of R containing a field of characteristic zero we show that if (V, Ï†) âŠ—R K is isotropic overâ€¦ (More)

Let R be a semi-local regular domain containing an infinite perfect subfield and let K be its field of fractions. Let G be a reductive semi-simple simply connected R-group scheme such that each ofâ€¦ (More)