Approximable triangulated categories


We will begin the talk with a theorem in algebraic geometry, about the relation between the derived categories \(D^b_{coh}(X)\) and \(D^{perf}(X)\) where \(X\) is a noetherian scheme. The theorem represents a major improvement over what was known.

It turns out that the result is a relatively straightforward corollary of the (somewhat technical) theorem that the category \(D_{qc}(X)\) is approximable. Approximability is a new notion, a recently introduced useful tool we will explain.

To illustrate the power of the new technique we will end the talk with several more applications, which we will then compare with what was known.


  • Professor Amnon Neeman
    Professor Amnon Neeman, Australian National University