
doi: 10.1017/fms.2015.16
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.
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
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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