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Noncommutative Geometry and Arithmetic

Marcolli, Matilde (2010) Noncommutative Geometry and Arithmetic. . http://resolver.caltech.edu/CaltechAUTHORS:20170712-133251099

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Abstract

This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. This talk concentrates on two main aspects: the relation of Stark numbers to the geometry of noncommutative tori with real multiplication, and the shadows of modular forms on the noncommutative boundary of modular curves, that is, the moduli space of on commutative tori.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1003.3662arXivDiscussion Paper
Additional Information:(Submitted on 18 Mar 2010).
Record Number:CaltechAUTHORS:20170712-133251099
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170712-133251099
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79018
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 Jul 2017 21:16
Last Modified:12 Jul 2017 21:16

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