Noncommutative geometry and arithmetics
- P. Almeida
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We intend to illustrate how the methods of noncommutative geometry are currently used to tackle problems in class field theory. Noncommutative geometry enables one to think geometrically in situations in which the classical notion of space formed of points is no longer adequate, and thus a “noncommutative space” is needed; a full account of this approach is given in  by its main contributor, Alain Connes. The class field theory, i.e., number theory within the realm of Galois theory, is undoubtedly one of the main achievements in arithmetics, leading to an important algebraic machinery; for a modern overview, see . The relationship between noncommutative geometry and number theory is one of the many themes treated in [22, 7–9, 11], a small part of which we will try to put in a more down-to-earth perspective, illustrating through an example what should be called an “application of physics to mathematics,” and our only purpose is to introduce nonspecialists to this beautiful area.
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- Noncommutative geometry and arithmetics
Russian Journal of Mathematical Physics
Volume 16, Issue 3 , pp 350-362
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- SP MAIK Nauka/Interperiodica
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- P. Almeida (1)
- Author Affiliations
- 1. Dep. de Matemática do Instituto Superior Técnico, Univ. Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal