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We prove useful necessary and sufficient conditions for an elliptic curve over a number field to admit a surjective adelic Galois representation.
Abelian l l -adic representations and elliptic curves , Research Notes in Mathematics, 7
Jean-Pierre Serre · 1968
Earlier work this paper cites.
“Propriétés galoisiennes des points d’ordre fini des courbes elliptiques.”
Jean-Pierre Serre · 1972
Earlier work this paper cites.
Frobenius distributions in GL 2 {\rm GL}_{2} -extensions
Serge Lang and Hale Trotter · 1976
Earlier work this paper cites.
“Modular curves and the Eisenstein ideal.”
B. Mazur · 1978
Earlier work this paper cites.
Algebraic number theory , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 322
Jürgen Neukirch · 1992
Cited alongside, same era.
Advanced topics in the arithmetic of elliptic curves , Graduate Texts in Mathematics, 151
Joseph H. Silverman · 1994
Cited alongside, same era.
“The MAGMA algebra system I: the user language.”
Wieb Bosma, John Cannon, and Catherine Playoust · 1997
Cited alongside, same era.
“Almost all elliptic curves are Serre curves.”
Nathan Jones
Cited in the paper.
“Elliptic curves with maximal Galois action on their torsion points.”
David Zywina
Cited in the paper.
“Elliptic curves with no exceptional primes.”
William Duke · 1997
Later among the works it cites.
Profinite groups , London Mathematical Society Monographs. New Series, 19
John S. Wilson · 1998
Later among the works it cites.
“Elliptic curves with surjective global Galois representation.”
Aaron Greicius · 2007
Later among the works it cites.
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