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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a desingularization of the moduli space of noncommutative tori
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by Igor Nikolaev PDF
Proc. Amer. Math. Soc. 136 (2008), 3769-3774 Request permission

Abstract:

It is shown that the moduli space of the noncommutative tori ${\mathbb A}_{\theta }$ admits a natural desingularization by the group $Ext~ ({\mathbb A}_{\theta },{\mathbb A}_{\theta })$. Namely, we prove that the moduli space of pairs $({\mathbb A}_{\theta }, Ext~ ({\mathbb A}_{\theta },{\mathbb A}_{\theta }))$ is homeomorphic to a punctured two-dimensional sphere. The proof is based on a correspondence (a covariant functor) between the complex and noncommutative tori.
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Additional Information
  • Igor Nikolaev
  • Affiliation: The Fields Institute for Mathematical Sciences, Toronto, Ontario, Canada
  • Email: igor.v.nikolaev@gmail.com
  • Received by editor(s): March 30, 2007
  • Received by editor(s) in revised form: September 6, 2007
  • Published electronically: June 24, 2008
  • Additional Notes: The author was partially supported by NSERC
  • Communicated by: Marius Junge
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3769-3774
  • MSC (2000): Primary 14H52, 46L85
  • DOI: https://doi.org/10.1090/S0002-9939-08-09465-3
  • MathSciNet review: 2425714