Algebra Seminar: Neeman -- Approximable triangulated categories

Amnon Neeman (ANU) 

Friday 7 September, 12-1pm, Place: Carslaw 375 

Title: Approximable triangulated categories 

Abstract: We will begin the talk with five new theorems in algebraic geometry,
statements about the derived categories $D^b_{coh}(X)$ and $D^{perf}(X)$ for schemes
$X$. Each of these theorems represents a major improvement over what was known. For
each of the five theorems special cases go back to results of Bondal and Van den Bergh,
Rickard and Rouquier. The short summary is that the old results all assumed equal
characteristic, the new results are the first to work in mixed characteristic. The more
detailed story is that, even in equal characteristic, our results are a sharp
improvement over what was known.  

It turns out that all these results are relatively straightforward corollaries of the
theorem that the category $D_{qc}(X)$ is approximable. This is a new notion we will
explain, and then illustrate its power.