Moscow Mathematical Journal

Volume 20, Issue 2, April–June 2020 pp. 277–309.

Smoothness of Derived Categories of Algebras

Authors: Alexey Elagin (1), Valery A. Lunts (2), and Olaf M. Schnürer (3)
Author institution:(1) Institute for Information Transmission Problems (Kharkevich Institute), Russian Federation;
National Research University Higher School of Economics, Russian Federation
(2) Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, IN 47405, USA;
National Research University Higher School of Economics, Russian Federation
(3) Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany

Summary:

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, thereby 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.

2010 Math. Subj. Class. Primary: 16E45; Secondary: 16E35, 14F05, 16H05.

Keywords: Differential graded category, derived category, generator, smoothness.

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