Embeddings of algebras in derived categories of surfaces

TL;DR

This paper investigates which finite-dimensional algebras with finite global dimension can have their derived categories embedded into the derived category of smooth projective surfaces, providing restrictions and explicit cases especially for hereditary algebras.

Contribution

It establishes new restrictions on algebras whose derived categories embed into surfaces and applies these to classify certain hereditary algebras.

Findings

Restrictions on algebras embeddable into surface derived categories

Explicit classification results for hereditary algebras

Insights into the structure of derived categories of surfaces

Abstract

By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some restrictions on those algebras whose derived categories can be embedded into the bounded derived category of a smooth projective surface. This is then applied to obtain explicit results for hereditary algebras.