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(1999)
In Applications of curves over finite fields (Seattle
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- Springer Journals
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- 10.1007/s40316-022-00208-7
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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 an one-sided divisibility result toward the Iwasawa main conjecture in this setting. The proof relies on the first and second reciprocity laws relating theta elements to Heegner point Euler systems on Shimura curves. As a by-product we also prove a result towards the rank 0 case of certain Bloch–Kato conjecture and a parity conjecture.
Journal
Annales mathématiques du Québec – Springer Journals
Published: Apr 1, 2023
Keywords: Iwasawa theory; p-adic L-functions; Shimura curves; Totally real field; Primary 11G40; Secondary 11G18