Some remarks on orbit sets of unimodular rows

We give a cohomological interpretation of orbit sets of unimodular rows of length d+1 over smooth algebras of Krull dimension d.Comment: 18 page

Stably free modules over smooth affine threefolds

We prove that the stably free modules over a smooth affine threefold over an algebraically closed field of characteristic different from 2 are free.Comment: 11 page

A degree map on unimodular rows

We associate to any endomorphism of the punctured affine space over some field an element in the Witt group of the base field that we call degree. We use this degree to give a counter-example to a question on unimodular rowsComment: Final version; J. Ramanujan Math. Soc. 27 (2012), no

The stable Adams operations on Hermitian K-theory

We prove that exterior powers of (skew-)symmetric bundles induce a $\lambda$-ring structure on the ring $GW^0(X) \oplus GW^2(X)$, when $X$ is a scheme where $2$ is invertible. Using this structure, we define stable Adams operations on Hermitian $K$-theory. As a byproduct of our methods, we also compute the ternary laws associated to Hermitian $K$-theory

Comparing Euler classes

We establish the equality of two definitions of an Euler class in algebraic geometry: the first definition is as a "characteristic class" with values in Chow-Witt theory, while the second definition is as an "obstruction class." Along the way, we refine Morel's relative Hurewicz theorem in A^1-homotopy theory, and show how to define (twisted) Chow-Witt groups for geometric classifying spaces.Comment: 33 pages; Final version (before proofs). To appear Q. J. Mat