For CM abelian varieties satisfying a simplicity hypothesis, Selmer ranks in p-th twists obey the symplectic or unitary distribution D^epsilon_q, giving unsolvability of most twisted Fermat curves along a fan structure.
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Selmer ranks in twists of CM abelian varieties
For CM abelian varieties satisfying a simplicity hypothesis, Selmer ranks in p-th twists obey the symplectic or unitary distribution D^epsilon_q, giving unsolvability of most twisted Fermat curves along a fan structure.