Vol. 11, No. 10, 2017

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Variation of anticyclotomic Iwasawa invariants in Hida families

Francesc Castella, Chan-Ho Kim and Matteo Longo

Vol. 11 (2017), No. 10, 2339–2368
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