@article{frengley-vemulapalli:tschirnhausen,
  title         = {Tschirnhausen bundles of quintic covers of $\mathbb{P}^1$},
  author        = {{Frengley}, Sam and {Vemulapalli}, Sameera},
  journal       = {arXiv e-prints},
  year          = 2025,
  pages         = {arXiv:2507.06942},
  url           = {https://doi.org/10.48550/arXiv.2507.06942}
}

@article{arangopineros-frengley-vemulapalli:galois-groups-tate-classes,
  title         = {Galois groups of simple abelian varieties over finite fields and exceptional {T}ate classes},
  author        = {{Arango-Pi{\~n}eros}, Santiago and {Frengley}, Sam and {Vemulapalli}, Sameera},
  journal       = {arXiv e-prints},
  year          = 2025,
  pages         = {arXiv:2505.09589},
  url           = {https://doi.org/10.48550/arXiv.2505.09589}
}

@article{corterealsantos-costello-frengley:ends,
  author        = {{Corte-Real Santos}, Maria and {Costello}, Craig and {Frengley}, Sam},
  title         = {Efficient algorithms for the detection of $(N,N)$-splittings and endomorphisms},
  journal       = {J. Cryptol.}
  year          = {2026},
  volume        = {39},
  doi           = {10.1007/s00145-025-09552-7},
  url           = {https://doi.org/10.1007/s00145-025-09552-7}
}

@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:2412.03358},
  url           = {https://doi.org/10.48550/arXiv.2412.03358}
}
    
@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,
  author        = {{Frengley}, Sam},
  title         = {Explicit $7$-torsion in the {Tate{\textendash}Shafarevich} groups of genus $2$ {Jacobians}},
  journal       = {J. Th\'eor. Nombres Bordx.},
  fjournal      = {Journal de th\'eorie des nombres de Bordeaux},
  pages         = {727--746},
  publisher     = {Soci\'et\'e Arithm\'etique de Bordeaux},
  volume        = {37},
  number        = {2},
  year          = {2025},
  doi           = {10.5802/jtnb.1340},
  url           = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1340/}
}

@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}
}