Beilinson-Kato元与p进l函数的插值

IF 0.5 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2021-10-08 DOI:10.1007/s40316-021-00172-8

Denis Benois, Kâzım Büyükboduk

{"title":"Beilinson-Kato元与p进l函数的插值","authors":"Denis Benois, Kâzım Büyükboduk","doi":"10.1007/s40316-021-00172-8","DOIUrl":null,"url":null,"abstract":"<div>Our objective in this series of two articles, of which the present article is the first, is to give a Perrin-Riou-style construction of p-adic L-functions (of Bellaïche and Stevens) over the eigencurve. As the first ingredient, we interpolate the Beilinson–Kato elements over the eigencurve (including the neighborhoods of \\(\\theta \\)-critical points). Along the way, we prove étale variants of Bellaïche’s results describing the local properties of the eigencurve. We also develop the local framework to construct and establish the interpolative properties of these p-adic L-functions away from \\(\\theta \\)-critical points.</div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 2","pages":"231 - 287"},"PeriodicalIF":0.5000,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-021-00172-8.pdf","citationCount":"1","resultStr":"{\"title\":\"Interpolation of Beilinson–Kato elements and p-adic L-functions\",\"authors\":\"Denis Benois, Kâzım Büyükboduk\",\"doi\":\"10.1007/s40316-021-00172-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>Our objective in this series of two articles, of which the present article is the first, is to give a Perrin-Riou-style construction of p-adic L-functions (of Bellaïche and Stevens) over the eigencurve. As the first ingredient, we interpolate the Beilinson–Kato elements over the eigencurve (including the neighborhoods of \\\\(\\\\theta \\\\)-critical points). Along the way, we prove étale variants of Bellaïche’s results describing the local properties of the eigencurve. We also develop the local framework to construct and establish the interpolative properties of these p-adic L-functions away from \\\\(\\\\theta \\\\)-critical points.</div>\",\"PeriodicalId\":42753,\"journal\":{\"name\":\"Annales Mathematiques du Quebec\",\"volume\":\"46 2\",\"pages\":\"231 - 287\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-10-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40316-021-00172-8.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematiques du Quebec\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40316-021-00172-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematiques du Quebec","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40316-021-00172-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

在这一系列的两篇文章中，本文是第一篇，我们的目标是给出特征曲线上p-adic L-函数（Bellaïche和Stevens）的Perrin-Riou式构造。作为第一个成分，我们在本征曲线上插值Beilinson–Kato元素（包括\（\θ\）-临界点的邻域）。在此过程中，我们证明了Bellaïche结果的étale变体，该结果描述了本征曲线的局部性质。我们还发展了局部框架来构造和建立这些p-adic L-函数在远离\（θ）-临界点处的插值性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Interpolation of Beilinson–Kato elements and p-adic L-functions

Our objective in this series of two articles, of which the present article is the first, is to give a Perrin-Riou-style construction of p-adic L-functions (of Bellaïche and Stevens) over the eigencurve. As the first ingredient, we interpolate the Beilinson–Kato elements over the eigencurve (including the neighborhoods of \(\theta \)-critical points). Along the way, we prove étale variants of Bellaïche’s results describing the local properties of the eigencurve. We also develop the local framework to construct and establish the interpolative properties of these p-adic L-functions away from \(\theta \)-critical points.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.