Algebraic Geometry Seminar

Amnon Neeman

"A non-commutative analog of extending a vector bundle from an open subset of a scheme"

For an open subscheme of a smooth scheme, Quillen proved there is a long exact sequence in K-theory. Thomason generalised this to fairly arbitrary singular schemes. In high dimensional topology, it turns out that one wants to consider a non-commutative version. Several people have studied this over the last 20 years. We will give a survey, and then discuss the improvements in a recent paper by Ranicki and the speaker.