Let B → A be a K-isogeny. Then exp(2[K : Q](h(B)− h(A)) (read: “change in height under isogeny”) is a rational number. ∗ For any individual prime `, the `-adic valuation of exp(2[K : Q](h(B)− h(A)) can be controlled by the Tate Conjecture. ∗ Using results of Raynaud, Faltings shows that for large `, depending only on the field K and the places S where A has… (More)
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