%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 }