arXiv Analytics

Sign in

arXiv:math/0212324 [math.AG]AbstractReferencesReviewsResources

On complex and noncommutative tori

Igor Nikolaev

Published 2002-12-23, updated 2004-09-23Version 2

The "noncommutative geometry" of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C*-algebras T_t={u,v | vu=exp(2\pi it)uv}, or noncommutative tori. The main result says that under the morphism isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra of Riemann surfaces.

Comments: 13 pages, straighten version, to appear Proc. Amer. Math. Soc
Journal: Proc. Amer. Math. Soc. 134 (2006), 973-981
Categories: math.AG, math.OA
Subjects: 14H52, 46L85
Related articles: Most relevant | Search more
arXiv:0706.4477 [math.AG] (Published 2007-06-29, updated 2009-04-07)
On a Teichmueller functor between the categories of complex tori and the Effros-Shen algebras
arXiv:math/0312449 [math.AG] (Published 2003-12-24, updated 2010-07-09)
Mapping class groups are linear
arXiv:1309.7202 [math.AG] (Published 2013-09-27, updated 2014-04-14)
Poisson varieties from Riemann surfaces

Links

Toolbox