On the modularity of rigid Calabi-Yau threefolds: epilogue
type: Item
instance of: scholarly article
title: On the modularity of rigid Calabi-Yau threefolds: epilogue
zbMATH Open document ID: 1290.14029
published in: Journal of Mathematical Sciences (New York)
publication date: 2014-01-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/0908.1210
review text: The modularity of rigid Calabi-Yau threefolds defined over \(\mathbb{Q}\) was established by \textit{F. Q. Gouvêa} and \textit{N. Yui} in [Expo. Math. 29, No. 1, 142--149 (2011; Zbl 1230.14056)]. Their proof rests on the Serre's conjecture (now a theorem) of the modularity of the residual two-dimensional Galois representations. This involves residual modularity in infinitely many characteristics. This article gives an alternative approach, namely, the author uses the residual modularity in a certain characteristic, and this is combined with the effective Chebotarev theorem.
reviewed by: Noriko Yui
Mathematics Subject Classification ID: 14J32
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 11F80
zbMATH DE Number: 6246153
zbMATH Keywords: rigid Calabi-Yau threefolds
zbMATH Keywords: modularity
author: Luis Dieulefait
MaRDI profile type: Publication
OpenAlex ID: W2026879701
arXiv ID: 0908.1210
cites work: The Tamagawa number conjecture of adjoint motives of modular forms
cites work: Q4462779
cites work: Q3424744
cites work: Serre's modularity conjecture. I
cites work: Serre's modularity conjecture. II
cites work: Modularity of 2-adic Barsotti-Tate representations
cites work: on l-adic representations attached to modular forms II
cites work: On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
cites work: On the meromorphic continuation of degree two \(L\)-functions
DOI: 10.1007/S10958-010-0175-8
description: scientific article; zbMATH DE number 6246153