Quantum arithmetic
Number Theory
2024-12-13 v1 Operator Algebras
Abstract
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the -algebras with real multiplication. Our construction fits all axioms of the quantum arithmetic conjectured by Manin and others. Applications to elliptic curves, Shafarevich-Tate groups of abelian varieties and height functions are reviewed.
Cite
@article{arxiv.2412.09148,
title = {Quantum arithmetic},
author = {Igor V. Nikolaev},
journal= {arXiv preprint arXiv:2412.09148},
year = {2024}
}
Comments
10 pages