A conjecture on the torsion points of elliptic curves with the complex multiplication
نویسنده
چکیده
Let GA be an AF -algebra given by a periodic Bratteli diagram with the incidence matrix A. Depending on a polynomial p(x) ∈ Z[x], we assign to GA a finite abelian group Abp(x)(GA) = Z /p(A)Z. It is shown that for every p(x), such that p(0) = ±1, the Abp(x)(GA) is an invariant of the strong stable isomorphism class of the AF -algebra GA. Using a categorical correspondence between the elliptic curves and the AF -algebras, a conjecture on the torsion points of an elliptic curve with the complex multiplication is formulated.
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