Variation of anticyclotomic Iwasawa invariants in Hida families

Castella, Francesc; Kim, Chan-Ho; Longo, Matteo

doi:10.2140/ant.2017.11.2339

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Variation of anticyclotomic Iwasawa invariants in Hida families

Francesc Castella, Chan-Ho Kim and Matteo Longo

Vol. 11 (2017), No. 10, 2339–2368

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 11R23

Secondary: 11F33

Milestones

Received: 9 January 2017

Revised: 5 September 2017

Accepted: 23 October 2017

Published: 31 December 2017

Authors

Francesc Castella
Department of Mathematics Princeton University Princeton, NJ United States

Chan-Ho Kim
School of Mathematics Korea Institute for Advanced Study (KIAS) Seoul South Korea

Matteo Longo
Dipartimento di Matematica Università di Padova Padova Italy

Vol. 11, No. 10, 2017