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Langlands reciprocity for the even-dimensional noncommutative tori
This article has been retracted


Author: Igor Nikolaev
Journal: Proc. Amer. Math. Soc. 139 (2011), 4153-4162
MSC (2010): Primary 11M55; Secondary 46L85
DOI: https://doi.org/10.1090/S0002-9939-2011-10864-5
Published electronically: April 13, 2011
MathSciNet review: 2823060
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Abstract:

The article "Langlands reciprocity for the even-dimensional noncommutative tori" by Igor Nikolaev (Proceedings of the American Mathematical Society 139 (2011), no. 12, 4153-4162) is retracted by the author on May 22, 2015 due to mathematical errors detected by the author at a later stage. The article was not withdrawn because of any errors or technical problems found by the reviewers or editors.

We conjecture an explicit formula for the higher-dimensional Dirichlet character; the formula is based on the $ K$-theory of the so-called noncommutative tori. It is proved that our conjecture is true for the two-dimensional and one-dimensional (degenerate) noncommutative tori. In the second case, one gets a noncommutative analog of the Artin reciprocity law.


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Additional Information

Igor Nikolaev
Affiliation: The Fields Institute for Research in Mathematical Sciences, Toronto, Ontario M5T 3J1, Canada
Address at time of publication: 616-315 Holmwood Avenue, Ottawa, ON, Canada, K1S 2R2
Email: igor.v.nikolaev@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2011-10864-5
Keywords: Langlands program, noncommutative tori
Received by editor(s): July 1, 2010
Received by editor(s) in revised form: October 7, 2010
Published electronically: April 13, 2011
Additional Notes: The author was partially supported by NSERC
Communicated by: Varghese Mathai
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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