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

Measurement of the nuclear modification factor of electrons from heavy-flavour hadron decays in Pb-Pb collisions at {\surd}sNN = 2.76 TeV with ALICE at the LHC

We present a measurement of the nuclear modification factor of electrons from heavy- flavour hadron decays at midrapidity in Pb-Pb collisions at {\surd}sNN = 2.76 TeV. Electrons are identified in the pt range 1.5 GeV/c < pt < 6 GeV/c. A suppression is seen for pt larger than 3.5 GeV/c in the most central collisions.Comment: 6 pages, 5 figures, EPIC@LHC - International Workshop on Early Physics with Heavy Ion Collisions at the LHC; Published by American Institute of Physics (AIP) in the Conference Proceedings Series (2011

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

Algebraic vector bundles on spheres

We determine the first non-stable ${\mathbb A}^1$-homotopy sheaf of $SL_n$. Using techniques of obstruction theory involving the ${\mathbb A}^1$-Postnikov tower, supported by some ideas from the theory of unimodular rows, we classify vector bundles of rank $\geq d-1$ on split smooth affine quadrics of dimension $2d-1$. These computations allow us to answer a question posed by Nori, which gives a criterion for completability of certain unimodular rows. Furthermore, we study compatibility of our computations of ${\mathbb A}^1$-homotopy sheaves with real and complex realization.Comment: 35 pages; final version (before page proofs) to appear J. Top. Significantly reorganized and incorporates some material from http://arxiv.org/abs/1204.0770 (which will also soon be replaced