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On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights (1909.12374v1)
Published 26 Sep 2019 in math.NT
Abstract: In this article, we study the Iwasawa theory for Hilbert modular forms over the anticyclotomic extension of a CM field. We prove a one sided divisibility result toward the Iwasawa main conjecture. The proof relies on the first and second reciprocity law relating theta elements to Heegner points Euler system. As a by-product we also prove certain Bloch-Kato type result in the rank $0$ case and a parity conjecture
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