Let be an elliptic curve, let be a fixed algebraic closure of , and let be the absolute Galois group of . The action of on the adelic Tate module of induces the adelic Galois representation
The goal of this paper is to explain how the image of 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 where the entanglement occurs over an abelian extension.
Cite this article
Harris B. Daniels, Alvaro Lozano-Robledo, Jackson S. Morrow, Towards a classification of entanglements of Galois representations attached to elliptic curves. Rev. Mat. Iberoam. 39 (2023), no. 3, pp. 803–844DOI 10.4171/RMI/1424