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Moscow Mathematical Journal, 2020, Volume 20, Number 2, Pages 277–309
DOI: https://doi.org/10.17323/1609-4514-2020-20-2-277-309 (Mi mmj765) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Smoothness of derived categories of algebras

Alexey Elaginab, Valery A. Luntscb, Olaf M. Schnürerd

a Institute for Information Transmission Problems (Kharkevich Institute), Russian Federation
b National Research University Higher School of Economics, Russian Federation
c Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, IN 47405, USA
d Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany
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DOI: https://doi.org/10.17323/1609-4514-2020-20-2-277-309
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, 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.
Key words and phrases: differential graded category, derived category, generator, smoothness.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
HSE Basic Research Program
Valery Lunts was supported in part by Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. No. 14.641.31.0001. Alexey Elagin's study has been funded within the framework of the HSE University Basic Research Program and the Russian Academic Excellence Project `5-100'.
Bibliographic databases:
Document Type: Article
MSC: Primary 16E45; Secondary 16E35, 14F05, 16H05
Language: English
Citation: Alexey Elagin, Valery A. Lunts, Olaf M. Schnürer, “Smoothness of derived categories of algebras”, Mosc. Math. J., 20:2 (2020), 277–309
Citation in format AMSBIB
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\paper Smoothness of derived categories of algebras
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\pages 277--309
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