关于平行权Hilbert模形式的反气旋Iwasawa主猜想

IF 0.5 Q3 MATHEMATICS Annales Mathematiques du Quebec Pub Date : 2022-11-09 DOI:10.1007/s40316-022-00208-7

Haining Wang

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引用次数: 3

摘要

在这篇文章中，我们研究了CM场反环原子扩展上Hilbert模形式的Iwasawa理论。在这种情况下，我们证明了岩泽主猜想的一个单侧可分性结果。证明依赖于将θ元素与Shimura曲线上的Heegner点Euler系统相关的第一和第二互易律。作为副产品，我们还证明了某个Bloch–Kato猜想和一个奇偶性猜想的秩为0的情况的一个结果。

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

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.

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来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

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0.00%

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期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.

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