Add to ORKGThis 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
Noncommutative geometry deals with many natural spaces for which the classical set-theoretic tools o...
Several recent results reveal a surprising connection between modular forms and noncommutative geome...
Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are...
This is an overview of recent results aimed at developing a geometry of noncommutative tori with rea...
We study the homogeneous coordinate rings of real multiplication noncommutative tori as defined by A...
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutati...
We describe the theory of complex multiplication on elliptic curves as it pertains to constructing a...
In this thesis we have tried to figure out some algebraic aspects of noncommutative tori, aiming at ...
This is the text of a series of five lectures given by the author at the "Second Annual Spring Insti...
One of the aims of algebraic number theory is to describe the field of algebraic numbers and the ex...
In this thesis we have tried to figure out some algebraic aspects of noncommutative tori, aiming at ...
In this project we explore the connections between elliptic curves, modular curves and complex multi...
We prove that the Shimizu L-function of a real quadratic field is obtained from a (Lorentzian) spect...
We give a new construction of noncommutative surfaces via elliptic difference operators, attaching a...
This text is written for the volume of the school/conference "Noncommutative Geometry 2005" held at ...
Noncommutative geometry deals with many natural spaces for which the classical set-theoretic tools o...
Several recent results reveal a surprising connection between modular forms and noncommutative geome...
Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are...
This is an overview of recent results aimed at developing a geometry of noncommutative tori with rea...
We study the homogeneous coordinate rings of real multiplication noncommutative tori as defined by A...
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutati...
We describe the theory of complex multiplication on elliptic curves as it pertains to constructing a...
In this thesis we have tried to figure out some algebraic aspects of noncommutative tori, aiming at ...
This is the text of a series of five lectures given by the author at the "Second Annual Spring Insti...
One of the aims of algebraic number theory is to describe the field of algebraic numbers and the ex...
In this thesis we have tried to figure out some algebraic aspects of noncommutative tori, aiming at ...
In this project we explore the connections between elliptic curves, modular curves and complex multi...
We prove that the Shimizu L-function of a real quadratic field is obtained from a (Lorentzian) spect...
We give a new construction of noncommutative surfaces via elliptic difference operators, attaching a...
This text is written for the volume of the school/conference "Noncommutative Geometry 2005" held at ...
Noncommutative geometry deals with many natural spaces for which the classical set-theoretic tools o...
Several recent results reveal a surprising connection between modular forms and noncommutative geome...
Yu. I. Manin conjectured that the maximal abelian extensions of the real quadratic number fields are...