Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P 1 , a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curve's jacobian in Weierstrass form and the covering map to its jacobian induced by the K-rational divisor at infinity. We give a unified account of all three cases.
Academic Press
Conjecture (Greenberg). Let K ∞ /K be the compositum of all Z p -extensions of K. Then the annilator of A has height at least two.A module whose annihilator has height at least 2 is said to be pseudo-null. Let E = O × K and U = p|p O × Kp , and denote by E the closure of E in U . The following theorem is a consequence of the main theorem of this paper, Theorem 26.
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