Quantum dynamics of elliptic curves

Published 10 Aug 2018 in math.NT and math.OA | (1808.03493v3)

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

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