Chennai Mathematical Institute


3:30 pm, Seminar Hall
Relative Picard groups and K-theory

Vivek Sadhu
Chennai Mathematical Institute.


The K-theoretical functors like Pic, K, NPic, NK etc. have been studied by various authors since 1960. In this talk, we will mainly focus on the behavior of these functors in the relative situation. In Particular, we will discuss some properties (e.g. Homotopy invariance, Bass fundamental theorem, etc.) of the groups K_{n}(f) and Pic(f) for a map of schemes f:X----> S. We will also discuss the Weibel K-dimension conjecture in negative K-theory and its relative version.