A Nonstandard Approach to Real Multiplication

Details A Nonstandard Approach to Real Multiplication A Nonstandard Approach to Real Multiplication

2006-12-07

arxiv.org/abs/math/0612184v2

Mathematics

Number Theory

20 pages. Adapted from a chapter of the author's PhD thesis

Scientific paper

We explore the possibility of using Model Theoretic ideas to study certain
non-Hausdorff spaces knwon as Quantum Tori with a view to their application to
Manin's theory of Real Multiplication. We study the morphisms between these
spaces using Nonstandard Analysis, and describe an action of a certain Galois
group on a certain classes of these spaces.

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