Thick subcategories on curves

TL;DR

This paper classifies thick subcategories within the bounded derived category of coherent sheaves on smooth projective curves over an algebraically closed field, advancing understanding of their categorical structure.

Contribution

It provides a complete classification of thick subcategories in the derived category of coherent sheaves on curves, a previously unresolved problem.

Findings

Complete classification of thick subcategories for curves

New insights into the structure of derived categories on algebraic curves

Framework applicable to further categorical studies in algebraic geometry

Abstract

We classify thick subcategories $\mathcal T \subset D^b(\mathrm{coh}\,C)$ for smooth projective curves $C$ over an algebraically closed field.