Triple product \(p\)-adic \(L\)-functions associated to finite slope \(p\)-adic families of modular forms
type: Item
instance of: scholarly article
title: Triple product \(p\)-adic \(L\)-functions associated to finite slope \(p\)-adic families of modular forms
zbMATH Open document ID: 1494.11046
DOI: 10.1215/00127094-2020-0076
author: Fabrizio Andreatta
author: Adrian Iovita
published in: Duke Mathematical Journal
publication date: 2021-07-08T00:00:00Z
review text: It is known for a while how to attach a \(p\)-adic \(L\)-function to a triple of Hida families (or ordinary \(p\)-adic families). However the definition of such \(p\)-adic \(L\)-function does not make sense in the case of finite slope \(p\)-adic families. This paper introduces a new method to handle the case of finite slope families. One views the finite slope families of modular forms as overconvergent sections of the modular sheaves. The construction is a geometric one. Indeed this is an application of a very general geometric construction that the authors developed, called the vector bundles with marked sections. In an earlier paper [Contrib. Math. Comput. Sci. 7, 401--441 (2014; Zbl 1328.11052)], \textit{E. Urban} had claimed a construction for the finite slope families. However this is a gap in that paper. In an appendix of this paper, Urban fixed the gap using results of this paper.
reviewed by: Zhengyu Mao
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11F85
zbMATH DE Number: 7369865
zbMATH Keywords: de Rham cohomology
zbMATH Keywords: overconvergent modular forms
zbMATH Keywords: overconvergent modular sheaves
zbMATH Keywords: \(p\)-adic \(L\)-functions
zbMATH Keywords: vector bundles with marked sections
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/00127094-2020-0076
OpenAlex ID: W3165627721
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description: scientific article; zbMATH DE number 7369865