Langlands reciprocity for the even dimensional noncommutative tori

Details Langlands reciprocity for the even dimensional noncommutative tori Langlands reciprocity for the even dimensional noncommutative tori

2010-04-06

arxiv.org/abs/1004.0904v3

Proc. Amer. Math. Soc. 139 (2011), 4153-4162

Mathematics

Operator Algebras

final version; to appear Proc. Amer. Math. Soc

Scientific paper

10.1090/S0002-9939-2011-10864-5

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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