SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS

Abstract : We prove for all $n$ less than or equal to 8 and under certain assumptions the equality predicted by the Iwasawa-Greenberg main conjecture between the characteristic power series of the Selmer group of the $2n$-th symmetric power twisted by $det^{-n}$ of the Galois representation associated to a Hida family and a congruence ideal for $Symm^n$ of this family.
Keywords : 11F33 11F80
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Submitted on : Friday, November 18, 2016 - 3:55:24 AM
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Haruzo Hida, Jacques Tilouine. SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS. 2016. ⟨hal-01398905⟩

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