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On the surjectivity of mod ℓ representat...

Zywina, David...

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On the surjectivity of mod ℓ representations associated to elliptic curves by Zywina, David ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	31-08-2015
Summary	Let E be an elliptic curve over the rationals that does not have complex multiplication. For each prime ℓ, the action of the absolute Galois group on the ℓ-torsion points of E can be given in terms of a Galois representation ρE,ℓ:Gal(Q¯/Q)→GL2(Fℓ). An important theorem of Serre says that ρE,ℓ is surjective for all sufficiently large ℓ. In this paper, we describe a simple algorithm based on Serre's proof that can quickly determine the finite set of primes ℓ for which ρE,ℓ is not surjective. We will also give some improved bounds for Serre's theorem.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.00
Total read	-
URL	http://arxiv.org/abs/1508.07661

Citation

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AMA 11th EditionReferences

Zywina, David. On the surjectivity of mod ℓ representations associated to elliptic curves. N.A. August 31, 2015. Accessed August 15, 2025. https://online.provdatabase.com/cite/18928

APA 7th EditionReferences

Zywina, David. (2015). On the surjectivity of mod ℓ representations associated to elliptic curves. N.A. https://online.provdatabase.com/cite/18928

Chicago 17th EditionReferences

Zywina, David. On the surjectivity of mod ℓ representations associated to elliptic curves. N.A. 2015. https://online.provdatabase.com/cite/18928

HarvardReferences

Zywina, David. (2015). On the surjectivity of mod ℓ representations associated to elliptic curves. [Online]. N.A. Available from: https://online.provdatabase.com/cite/18928. (Accessed 15 August 2025).

Harvard AustraliaReferences

Zywina, David, 2015, On the surjectivity of mod ℓ representations associated to elliptic curves, N.A, viewed 15 August 2025, <https://online.provdatabase.com/cite/18928>

MLA 9th EditionWorks Cited

Zywina, David. On the surjectivity of mod ℓ representations associated to elliptic curves. N.A, 2015. PROV Database, https://online.provdatabase.com/cite/18928.

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