Kyoto Journal of Mathematics

The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication

Takashi Hara and Tadashi Ochiai

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Abstract

We deduce the cyclotomic Iwasawa main conjecture for Hilbert modular cusp forms with complex multiplication from the multivariable main conjecture for CM number fields. To this end, we study in detail the behavior of the p-adic L-functions and the Selmer groups attached to CM number fields under specialization procedures.

Article information

Source
Kyoto J. Math., Volume 58, Number 1 (2018), 1-100.

Dates
Received: 23 July 2015
Revised: 21 April 2016
Accepted: 19 July 2016
First available in Project Euclid: 15 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1518685212

Digital Object Identifier
doi:10.1215/21562261-2017-0018

Mathematical Reviews number (MathSciNet)
MR3776280

Zentralblatt MATH identifier
06873129

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

Keywords
Iwasawa main conjecture Hilbert modular forms p-adic L-functions Selmer groups complex multiplication

Citation

Hara, Takashi; Ochiai, Tadashi. The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication. Kyoto J. Math. 58 (2018), no. 1, 1--100. doi:10.1215/21562261-2017-0018. https://projecteuclid.org/euclid.kjm/1518685212


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