Algebraic geometry: Raga Bhimpalasi: The Vaserstein-Suslin Jugalbandhi
by Ravi Rao (Tata Inst. Fund. Res.) in Eckhart 202
The
study of unimodular rows, and their orbit spaces, over a commutative ring
with $1$, lies in the fertile cross-section of ideas from Algebra, Algebraic
Topology, Number Theory, and Algebraic Geometry. Witt group structures, Cohomotopy
groups, Mennicke symbols, Reciprocity Laws, etc. make their appearance very
naturally. We shall discuss the connection of the study of orbit spaces,
via a symbiosis of constructions of L.N. Vaserstein, A. Suslin, and its relation
to problems in classical K-theory, and to the program of J.-P. Serre, which
interconnected the study of projective $R$-modules with problems of efficient
generation of ideals of $R$.