Smoothness of Derived Categories of Algebras

TL;DR

This paper proves the smoothness of the bounded derived categories of certain finite-dimensional algebras over perfect fields, providing a general criterion for smoothness in the dg sense.

Contribution

It establishes the smoothness of derived categories for a broad class of algebras over perfect fields, answering a question of Iyama.

Findings

Smoothness holds for finite-dimensional algebras over perfect fields.

General criterion for smoothness of derived categories.

Answers to Iyama's question on algebra smoothness.

Abstract

We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for any algebra over a perfect field that is finite over its center and whose center is finitely generated as an algebra. These results are deduced from a general sufficient criterion for smoothness.