| Details: |
ABSTRACT. Let R be a commutative Noetherian ring of dimension n. A row (a1, · · · , ak)
in R
k
is said to be unimodular if there exist b1, · · · , bk ∈ R such that Pn
i=1 aibi = 1. Let
Umn+1(R)/En+1(R) be the orbit space of unimodular rows of length n + 1 under the
natural action of elementary (n + 1) × (n + 1) matrices. This space is equipped with a
group structure, introduced by van der Kallen.
In this talk, we study the group Umn+1(R)/En+1(R) when R is the coordinate ring of
a smooth real affine variety. |