Imperial College London
Professor David Helm

ProfessorDavidHelm

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

d.helm

 
 
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Location

 

672Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@unpublished{Allen:2022,
author = {Allen, PB and Calegari, F and Caraiani, A and Gee, T and Helm, D and Hung, BVL and Newton, J and Scholze, P and Taylor, R and Thorne, JA},
publisher = {arXiv},
title = {Potential automorphy over CM fields},
url = {https://arxiv.org/abs/1812.09999v2},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - UNPB
AB  - Let $F$ be a CM number field. We prove modularity lifting theorems forregular $n$-dimensional Galois representations over $F$ without anyself-duality condition. We deduce that all elliptic curves $E$ over $F$ arepotentially modular, and furthermore satisfy the Sato--Tate conjecture. As anapplication of a different sort, we also prove the Ramanujan Conjecture forweight zero cuspidal automorphic representations for$\mathrm{GL}_2(\mathbf{A}_F)$.
AU  - Allen,PB
AU  - Calegari,F
AU  - Caraiani,A
AU  - Gee,T
AU  - Helm,D
AU  - Hung,BVL
AU  - Newton,J
AU  - Scholze,P
AU  - Taylor,R
AU  - Thorne,JA
PB  - arXiv
PY  - 2022///
TI  - Potential automorphy over CM fields
UR  - https://arxiv.org/abs/1812.09999v2
UR  - http://hdl.handle.net/10044/1/77441
ER  -
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