ENGLISH

Arithmetic Noncommutative Geometry

By Matilde Marcolli

Book information

Publisher
American Mathematical Society
Year
2005
ISBN
0821838334, 9780821838334
Open Library ID
OL16130260M
Language
english
Format
PDF
Filesize
926 kB (947842 bytes)
Series
University Lecture Series
Pages
129\129
Topic
Mathematics\\Geometry and Topology
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

Marcolli works from her invited lectures delivered at several universities to address questions and reinterpret results and constructions from number theory and arithmetric algebraic geometry, generally is they are applied to the geometry and arithmetic of modular curves and to the fibers of archimedean places of arithmetic surfaces and varieties. One of the results is to refine the boundary structure of certain classes of spaces, such as moduli spaces (like modular curves) or arithmetric varieties completed by suitable fibers at infinity by adding boundaries that are not visible within algebraic geometry. Marcolli defines the noncommutative spaces and spectral triples, then describes noncommutable modular curves, quantum statistical mechanics and Galois theory, and noncommutative geometry at arithmetric infinity.

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