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Forum of Mathematics, Sigma
Article . 2015 . Peer-reviewed
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Forum of Mathematics, Sigma
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THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS

The Iwasawa main conjecture for Hilbert modular forms
Authors: XIN WAN;

THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS

Abstract

Following the ideas and methods of a recent work of Skinner and Urban, we prove the one divisibility of the Iwasawa main conjecture for nearly ordinary Hilbert modular forms under certain local hypotheses. As a consequence, we prove that for a Hilbert modular form of parallel weight, trivial character, and good ordinary reduction at all primes dividing$p$, if the central critical$L$-value is zero then the$p$-adic Selmer group of it has rank at least one. We also prove that one of the local assumptions in the main result of Skinner and Urban can be removed by a base-change trick.

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Keywords

Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, 16W10 (primary), critical \(L\)-value, QA1-939, 16D50 (secondary), \(p\)-adic Selmer group, Iwasawa main conjecture, Mathematics, Iwasawa theory, Hilbert modular forms

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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
23
Top 10%
Top 10%
Top 10%
Published in a Diamond OA journal