A Nonstandard Approach to Real Multiplication
Lawrence Taylor
TL;DR
This paper investigates the use of Model Theoretic and Nonstandard Analysis techniques to study Quantum Tori and their relation to Manin's Real Multiplication theory, revealing new structural insights.
Contribution
It introduces a novel nonstandard approach to analyze Quantum Tori and their morphisms, connecting model theory with number theory.
Findings
Describes morphisms between Quantum Tori using Nonstandard Analysis
Establishes an action of a Galois group on classes of Quantum Tori
Provides new perspectives on Real Multiplication through nonstandard methods
Abstract
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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Taxonomy
TopicsMathematical and Theoretical Analysis · History and Theory of Mathematics · Computability, Logic, AI Algorithms