Quantum dynamics of elliptic curves

Igor V. Nikolaev

doi:10.1007/s00010-025-01165-6

Quantum dynamics of elliptic curves

Number Theory 2025-09-24 v3 Operator Algebras

Authors: Igor V. Nikolaev

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Abstract

We calculate K-theory of a crossed product $C^*$ -algebra of the noncommutative torus with real multiplication by elliptic curve $\mathscr{E}(K)$ over a number field $K$ . This result is used to evaluate the rank and the Shafarevich-Tate group of $\mathscr{E}(K)$ .

Keywords

elliptic curves algebraic k-theory quantum groups

Cite

@article{arxiv.1808.03493,
  title  = {Quantum dynamics of elliptic curves},
  author = {Igor V. Nikolaev},
  journal= {arXiv preprint arXiv:1808.03493},
  year   = {2025}
}

Comments

to appear in Aequationes Mathematicae

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