# Panagiotis Kostas: The derived category of coherent sheaves and Rouquier dimension of triangulated categories

**Time: **
Mon 2021-08-23 12.00 - 13.00

**Location: **
Zoom, meeting ID: 697 4204 2109 (password required, contact arias@math.su.se)

**Respondent: **
Panagiotis Kostas

**Abstract:** The purpose of this thesis is twofold. On one hand, we introduce the basic theory on the bounded derived category of coherent sheaves on a scheme *X* and prove a result of Beilinson on the structure of the derived category of \(\mathbb{P}^n\). On the other hand, we introduce the Rouquier dimension of a triangulated category and present a conjecture by Orlov, stating that, under some conditions, one can recover the dimension of a scheme by looking at its bounded derived category.