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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 4, Pages 50–83
DOI: https://doi.org/10.4213/faa4233
(Mi faa4233)
 

Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves

Dmitri Orlov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
References:
Abstract: New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and that the resulting DG algebras are smooth. This description allows us to show that some of these DG algebras determine smooth proper noncommutative curves that provide smooth minimal noncommutative resolutions for singular rational curves.
Keywords: noncommutative algebraic geometry, derived noncommutative schemes, differential graded algebras, perfect modules and complexes.
Received: 07.05.2024
Revised: 25.06.2024
Accepted: 26.06.2024
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 4, Pages 384–408
DOI: https://doi.org/10.1134/S001626632404004X
Document Type: Article
Language: Russian
Citation: Dmitri Orlov, “Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves”, Funktsional. Anal. i Prilozhen., 58:4 (2024), 50–83; Funct. Anal. Appl., 58:4 (2024), 384–408
Citation in format AMSBIB
\Bibitem{Orl24}
\by Dmitri Orlov
\paper Twisted tensor product, smooth DG algebras, and~noncommutative resolutions of singular curves
\jour Funktsional. Anal. i Prilozhen.
\yr 2024
\vol 58
\issue 4
\pages 50--83
\mathnet{http://mi.mathnet.ru/faa4233}
\crossref{https://doi.org/10.4213/faa4233}
\transl
\jour Funct. Anal. Appl.
\yr 2024
\vol 58
\issue 4
\pages 384--408
\crossref{https://doi.org/10.1134/S001626632404004X}
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    Функциональный анализ и его приложения Functional Analysis and Its Applications
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