Let G=(V,E) be an undirected graph. Given ℓ∈\Z, let m:V→\Z+ be a non-negative integer valued function satisfying
As an application of Theorem 5.1, in this final section we prove results on the growth of Selmer and Mordell–Weil groups along the finite layers of K∞/K.
A natural question to ask is whether or not the analogue of Corollary 3.4 or Corollary 4.4 holds with Pic(−)Q replaced by Pic(−)Qp. We will show in the section that when k is a finite field this cannot be the case, since it would imply Tate’s isogen…
In this section, we prove the main results of this article, that are Theorem 3 about existence of solutions to (3) and Theorem 4 about uniqueness.
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