SMS scnews item created by Ulrich Thiel at Fri 31 Aug 2018 1811
Type: Seminar
Distribution: World
Expiry: 12 Oct 2018
Calendar1: 7 Sep 2018 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Neeman -- Approximable triangulated categories
Auth: thiel@1.128.109.14 (uthi9031) in SMS-WASM

# 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.


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