Coleman族的形式模型及其在Iwasawa不变量中的应用

IF 0.5 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2023-07-06 DOI:10.1007/s40316-023-00217-0

Filippo Alberto Edoardo Nuccio Mortarino Majno di Capriglio, Tadashi Ochiai, Jishnu Ray

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引用次数: 0

摘要

对于给定模块形式的科尔曼族，我们构建了一个形式模型，并证明了与科尔曼族相关的伽罗瓦表示族的存在。作为应用，我们研究了在模块形式的科尔曼族中\(\mathbb {Q}\)的循环\(\mathbb {Z}_p\)-extension of \(\mathbb {Q}\)上的对偶精细（严格）塞尔默群的岩沢（\lambda）-和（\mu）-不变量的变化。这概括了 Jha 和 Sujatha 早期针对希达族的工作。

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A formal model of Coleman families and applications to Iwasawa invariants

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A formal model of Coleman families and applications to Iwasawa invariants

For a given Coleman family of modular forms, we construct a formal model and prove the existence of a family of Galois representations associated to the Coleman family. As an application, we study the variations of Iwasawa \(\lambda \)- and \(\mu \)-invariants of dual fine (strict) Selmer groups over the cyclotomic \(\mathbb {Z}_p\)-extension of \(\mathbb {Q}\) in Coleman families of modular forms. This generalizes an earlier work of Jha and Sujatha for Hida families.

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来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

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.