Arithmetic Noncommutative Geometry

The main focus of these lecture notes is an interpretation of the arithmetic of modular curves and archimedean fibers of arithmetic varieties in the realm of non-commutative geometry. The first chapter reviews the basic notions of non-commutative geometry. The second chapter discusses properties of modular curves from the point of view of a description of their boundary strata in the framework of non-commutative geometry. The third chapter includes a discussion of the non-commutative space of commensurability classes of Q-lattices and its relation to class field theory. The fourth and last chapter involves the non-commutative geometry of the fibers at arithmetic infinity of varieties (surfaces) over number fields. The book aims to introduce and link together a variety of general concepts from geometry, number theory and physics. Many proofs have not been included in the text.

Reviewer: 
pso
Book details
Author:  Publisher: 
Published: 
2005
ISBN: 
0-8218-3833-4
Price: 
USD 29
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