Open Access
Translator Disclaimer
2017 Variation of anticyclotomic Iwasawa invariants in Hida families
Francesc Castella, Chan-Ho Kim, Matteo Longo
Algebra Number Theory 11(10): 2339-2368 (2017). DOI: 10.2140/ant.2017.11.2339

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.

Citation

Download Citation

Francesc Castella. Chan-Ho Kim. Matteo Longo. "Variation of anticyclotomic Iwasawa invariants in Hida families." Algebra Number Theory 11 (10) 2339 - 2368, 2017. https://doi.org/10.2140/ant.2017.11.2339

Information

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

zbMATH: 06825453
MathSciNet: MR3744359
Digital Object Identifier: 10.2140/ant.2017.11.2339

Subjects:
Primary: 11R23
Secondary: 11F33

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

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.11 • No. 10 • 2017
MSP
Back to Top