Classical correspondences between per-prime Tate curves: a matching obstruction
For the complex Tate curves E_p = C*/p^Z attached to primes, we compute the classical divisorial correspondence groups. For distinct primes, Hom(E_p,E_q) is nonzero exactly when log(p)log(q) belongs to 4 pi^2 Q. If log(p)log(q)/(4 pi^2) = u/v in lowest positive terms, this group has rank one and its generator has isogeny degree uv. The isogeny relation between distinct primes is a partial matching: unconditionally, each prime has at most one partner. These rigidity statements specialize results of Winkelmann; the explicit Hom generator and degree are included here. Outside the matching, the…
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