Number Theory Seminar
Matthew Morrow
University of Chicago
Pro-excision in algebraic K-theory
Abstract: It has been known since the early days of algebraic K-theory that it fails to satisfy excision
for example, the difference between the K-theory of a singular curve and its normalisation is not determined by the
conductor ideal and it is now known that the precise obstruction to this may be described using cyclic or topological
cyclic homology. However, this obstruction vanishes in all cases of interest in algebraic and arithmetic geometry if one
passes to formal infinitesimal thickenings in a suitable sense, and this is sufficient for many applications.
I will begin with an introduction to algebraic K-theory, then explain this infinitesimal excision result, and finally
indicate the applications within algebraic geometry (which are joint with Amalendu Krishna).
Tuesday January 29, 2013 at 3:00 PM in SEO 636