@article{arangopineros-frengley-vemulapalli:galois-groups-of-avs, title = {Galois groups of low dimensional abelian varieties over finite fields}, author = {{Arango-Pi{\~n}eros}, Santiago and {Frengley}, Sam and {Vemulapalli}, Sameera}, journal = {arXiv e-prints}, year = 2024, pages = {arXiv:}, url = {https://doi.org/}, } @article{frengley:geometry-humbert, title = {On the geometry of the Humbert surface of square discriminant}, author = {{Frengley}, Sam}, journal = {arXiv e-prints}, year = 2024, pages = {arXiv:2408.09830}, url = {https://doi.org/10.48550/arXiv.2408.09830}, } @article{frengley:explicit-7-tors-in-sha, title = {Explicit $7$-torsion in the Tate-Shafarevich groups of genus $2$ Jacobians}, author = {{Frengley}, Sam}, journal = {arXiv e-prints}, year = 2024, pages = {arXiv:2405.11693}, url = {https://doi.org/10.48550/arXiv.2403.03191}, } @article{cowan-frengley-martin:generic-models-for-rm, title = {Generic models for genus 2 curves with real multiplication}, author = {{Cowan}, Alex and {Frengley}, Sam and {Martin}, Kimball}, journal = {arXiv e-prints}, keywords = {Mathematics - Number Theory, Mathematics - Algebraic Geometry}, year = 2024, month = mar, pages = {arXiv:2403.03191}, url = {https://doi.org/10.48550/arXiv.2403.03191}, } @inproceedings{corterealsantos-costello-frengley:NN-splittings, author = {{Corte-Real Santos}, Maria and {Costello}, Craig and {Frengley}, Sam}, editor = {{Tang}, Qiang and {Teague}, Vanessa}, title = {An {A}lgorithm for {E}fficient {D}etection of $(N,N)$-{S}plittings and {I}ts {A}pplication to the {I}sogeny {P}roblem in {D}imension 2}, booktitle = {Public-Key Cryptography -- PKC 2024}, year = {2024}, publisher = {Springer Nature Switzerland}, address = {Cham}, pages = {157--189} } @article{frengley:12-congs, author = {Frengley, Sam}, title = {On $12$-congruences of elliptic curves}, journal = {Int. J. Number Theory}, fjournal = {International Journal of Number Theory}, volume = {20}, year = {2024}, number = {2}, pages = {565--601}, issn = {1793-0421,1793-7310}, mrclass = {11G05 (11F80)}, mrnumber = {4709643}, doi = {10.1142/S1793042124500301}, url = {https://doi.org/10.1142/S1793042124500301}, } @article{frengley:congs-of-ell-crv-nonsurj-reps, title = {Congruences of elliptic curves arising from nonsurjective mod {$N$} {G}alois representations}, author = {{Frengley}, Sam}, year = 2023, journal = {Math. Comp.}, volume = 92, number = 339, pages = {409--450}, doi = {10.1090/mcom/3770}, issn = {0025-5718}, url = {https://doi.org/10.1090/mcom/3770}, fjournal = {Mathematics of Computation}, mrclass = {11G05}, mrnumber = 4496970 } @phdthesis{frengley:thesis, title = {Explicit moduli spaces for curves of genus 1 and 2}, author = {{Frengley}, Samuel}, year = {2023}, month = {December}, school = {University of Cambridge}, type = {PhD thesis}, url = {https://www.repository.cam.ac.uk/handle/1810/369243}, doi = {10.17863/CAM.109127}, keywords = {Arithmetic Geometry, Elliptic curves, Galois representations, Hilbert modular surfaces, Modular curves, Number Theory} }