On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights

Haining Wang

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arXiv · 1909.12374

On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights

Haining Wang

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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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Haining Wang. 2019-09-26. On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights. https://arxiv.org/abs/1909.12374

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