Title	Modularity of elliptic curves over totally real quartic fields not containing the square root of 5
Creator	Box, Josha
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2020-09-04T10:02
Description	Following Wiles's breakthrough work, it has been shown in recent years that elliptic curves over each totally real field of degree 2 (Freitas-Le Hung-Siksek) or 3 (Derickx-Najman-Siksek) are modular. We study the degree 4 case and show that if K is a totally real quartic field in which 5 is not a square, then every elliptic curve over K is modular. Thanks to strong results of Thorne and Kalyanswami, this boils down to the determination of all quartic points on a few modular curves. Some of these curves have infinitely many quartic points. In this talk I will discuss how Chabauty's method and sieving can nevertheless be used to describe such points.
Extent	25.0 minutes
Subject	Mathematics; Number theory; Algebraic geometry; Arithmetic number theory
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Warwick
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2021-03-04
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0396032
URI	http://hdl.handle.net/2429/77446
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Graduate
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Modularity of elliptic curves over totally real quartic fields not containing the square root of 5 Box, Josha

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