Matthew Morrow : Pro-excision in algebraic K-theory

Posted by Majid Hadian-Jazi , part of the Number Theory Seminar.

At

Jan. 29, 2013, 3 p.m.

In

SEO 636

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).