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Fields of definition of elliptic k-curves and the realizability of all genus 2 sato–tate groups over a number field

Author
Fite, F.; Guitart, X.
Type of activity
Journal article
Journal
Transactions of the American Mathematical Society
Date of publication
2018-07-01
Volume
370
First page
4623
Last page
4659
DOI
10.1090/tran/7074
Project funding
Arithmetic of L functions and Galois structures
Repository
http://hdl.handle.net/2117/131241 Open in new window
http://www.maia.ub.es/~guitart/index_files/Isoclass.pdf Open in new window
URL
http://www.ams.org/journals/tran/2018-370-07/S0002-9947-2018-07074-X/ Open in new window
Abstract
Let A/Q be an abelian variety of dimension g = 1 that is isogenous over Q to Eg, where E is an elliptic curve. If E does not have complex multiplication (CM), by results of Ribet and Elkies concerning fields of definition of elliptic Q-curves E is isogenous to a curve defined over a polyquadratic extension of Q. We show that one can adapt Ribet’s methods to study the field of definition of E up to isogeny also in the CM case. We find two applications of this analysis to the theory of Sato–Ta...
Citation
Fite, F.; Guitart, X. Fields of definition of elliptic k-curves and the realizability of all genus 2 sato–tate groups over a number field. "Transactions of the American Mathematical Society", 1 Juliol 2018, vol. 370, p. 4623-4659.
Group of research
TN - Number Theory Research Group

Participants

  • Fite Naya, Francesc  (author)
  • Guitart Morales, Xavier  (author)

Attachments