## Algebra & Number Theory

### Variation of anticyclotomic Iwasawa invariants in Hida families

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ant/1517454187

Digital Object Identifier
doi:10.2140/ant.2017.11.2339

Mathematical Reviews number (MathSciNet)
MR3744359

Zentralblatt MATH identifier
06825453

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

#### Citation

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. https://projecteuclid.org/euclid.ant/1517454187

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