I. Nikolaev. (2009)cite arxiv:0910.3875
Comment: 9 pages; written from scratch.
Abstract
We construct an inverse of functor F, which maps isomorphism classes of
elliptic curves with complex multiplication to the stable isomorphism classes
of the so-called noncommutative tori with real multiplication. The construction
allows to prove, that complex and real multiplication are mirror symmetric,
i.e. F maps each imaginary quadratic field of discriminant -D to the real
quadratic field of discriminant D.
%0 Generic
%1 Nikolaev2009
%A Nikolaev, Igor
%D 2009
%K curves modular multiplication real
%T Real multiplication and modular curves
%U http://arxiv.org/abs/0910.3875
%X We construct an inverse of functor F, which maps isomorphism classes of
elliptic curves with complex multiplication to the stable isomorphism classes
of the so-called noncommutative tori with real multiplication. The construction
allows to prove, that complex and real multiplication are mirror symmetric,
i.e. F maps each imaginary quadratic field of discriminant -D to the real
quadratic field of discriminant D.
@misc{Nikolaev2009,
abstract = { We construct an inverse of functor F, which maps isomorphism classes of
elliptic curves with complex multiplication to the stable isomorphism classes
of the so-called noncommutative tori with real multiplication. The construction
allows to prove, that complex and real multiplication are mirror symmetric,
i.e. F maps each imaginary quadratic field of discriminant -D to the real
quadratic field of discriminant D.
},
added-at = {2011-02-17T07:26:48.000+0100},
author = {Nikolaev, Igor},
biburl = {https://www.bibsonomy.org/bibtex/2810cbab5a890ed90935450d9ba6aeee1/uludag},
description = {Real multiplication and modular curves},
interhash = {50d63a8018797e32ef60fcb09495e0e2},
intrahash = {810cbab5a890ed90935450d9ba6aeee1},
keywords = {curves modular multiplication real},
note = {cite arxiv:0910.3875
Comment: 9 pages; written from scratch},
timestamp = {2011-02-17T07:26:48.000+0100},
title = {Real multiplication and modular curves},
url = {http://arxiv.org/abs/0910.3875},
year = 2009
}