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arXiv · 1808.03493

Quantum dynamics of elliptic curves

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 $\mathscr{E}(K)$.

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Igor V. Nikolaev. 2018-08-10. Quantum dynamics of elliptic curves. https://doi.org/10.1007/s00010-025-01165-6

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