Real Multiplication and noncommutative geometry
| dc.creator | Manin, Yuri I. | |
| dc.date | 2002-02-12 | |
| dc.date.accessioned | 2026-07-07T04:46:24Z | |
| dc.date.available | 2026-07-07T04:46:24Z | |
| dc.description | Classical theory of Complex Multiplication (CM) shows that all abelian extensions of a complex quadratic field $K$ are generated by the values of appropriate modular functions at the points of finite order of elliptic curves whose endomorphism rings are orders in $K$. For real quadratic fields, a similar description is not known. However, the relevant (still unproved) case of Stark conjectures ([St1]) strongly suggests that such a description must exist. In this paper we propose to use two--dimensional quantum tori corresponding to real quadratic irrationalities as a replacement of elliptic curves with complex multiplication. We discuss some basic constructions of the theory of quantum tori from the perspective of this Real Multiplication (RM) research project. | |
| dc.description | 46 pp., amstex file, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0202109 | |
| dc.identifier | http://arxiv.org/abs/math/0202109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63320 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Real Multiplication and noncommutative geometry | |
| dc.type | text |