Remarks on generators and dimensions of triangulated categories

TL;DR

This paper establishes that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is exactly one and explores the spectrum of these dimensions.

Contribution

It proves a precise dimension value for derived categories on curves and discusses their dimension spectrums, advancing understanding of their structure.

Findings

Dimension of derived category on curves is exactly one.

Discusses the spectrum of dimensions in these categories.

Abstract

In this paper we prove that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is equal to one. We also discuss dimension spectrums of these categories.