Papers › Towards a classification of entanglements of Galois representations attached to elliptic curves
Towards a classification of entanglements of Galois representations attached to elliptic curves
Harris B. Daniels, Álvaro Lozano-Robledo, Jackson S. Morrow
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Let E/ℚ be an elliptic curve, let ℚ be a fixed algebraic closure of ℚ, and let G_ℚ=Gal(ℚ/ℚ) be the absolute Galois group of ℚ. The action of G_ℚ on the adelic Tate module of E induces the adelic Galois representation ρ_EG_ℚ →GL(2,ℤ). The goal of this paper is to explain how the image of ρ_E can be smaller than expected. To this end, we offer a group theoretic categorization of different ways in which an entanglement between division fields can be explained and prove several results on elliptic curves (and more generally, principally polarized abelian varieties) over ℚ where the entanglement occurs over an abelian extension.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections