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Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms

  • Kâzım Büyükboduk und Antonio Lei ORCID logo EMAIL logo
Veröffentlicht/Copyright: 13. Dezember 2017

Abstract

This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic p-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson–Flach elements.

MSC 2010: 11R23; 11F11; 11R20

Communicated by Jan Bruinier


Funding source: European Commission

Award Identifier / Grant number: 745691

Award Identifier / Grant number: 05710

Funding statement: The first author is partially supported by the European Commission Global Fellowship CriticalGZ. The second author is supported by the NSERC Discovery Grants Program 05710.

Acknowledgements

We would like to thank Henri Darmon and Chan-Ho Kim for enlightening discussions during the preparation of this paper, and the anonymous referees for the suggestions and comments on a previous version of this paper.

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Received: 2016-02-26
Revised: 2017-10-31
Published Online: 2017-12-13
Published in Print: 2018-07-01

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