1,129 research outputs found
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
-ring structure on the ring , when is a
scheme where is invertible. Using this structure, we define stable Adams
operations on Hermitian -theory. As a byproduct of our methods, we also
compute the ternary laws associated to Hermitian -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
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