# 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.
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https://hal.archives-ouvertes.fr/hal-01398905
Contributor : Jacques Tilouine <>
Submitted on : Friday, November 18, 2016 - 3:55:24 AM
Last modification on : Wednesday, February 6, 2019 - 1:22:59 AM
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• HAL Id : hal-01398905, version 1

### Citation

Haruzo Hida, Jacques Tilouine. SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS. 2016. ⟨hal-01398905⟩

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