Algebra & Number Theory

Variation of anticyclotomic Iwasawa invariants in Hida families

Francesc Castella, Chan-Ho Kim, and Matteo Longo

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Building on the construction of big Heegner points in the quaternionic setting by Longo and Vigni, and their relation to special values of Rankin–Selberg L -functions established by Castella and Longo, we obtain anticyclotomic analogues of the results of Emerton, Pollack and Weston on the variation of Iwasawa invariants in Hida families. In particular, combined with the known cases of the anticyclotomic Iwasawa main conjecture in weight 2 , our results yield a proof of the main conjecture for p -ordinary newforms of higher weights and trivial nebentypus.

Article information

Algebra Number Theory, Volume 11, Number 10 (2017), 2339-2368.

Received: 9 January 2017
Revised: 5 September 2017
Accepted: 23 October 2017
First available in Project Euclid: 1 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R23: Iwasawa theory
Secondary: 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]

Iwasawa theory Hida theory Selmer groups Heegner points special values of $L$-functions


Castella, Francesc; Kim, Chan-Ho; Longo, Matteo. Variation of anticyclotomic Iwasawa invariants in Hida families. Algebra Number Theory 11 (2017), no. 10, 2339--2368. doi:10.2140/ant.2017.11.2339.

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