@misc{CocciaLitt,
  author = {Coccia, Simone and Litt, Daniel},
  title = {Density of integral points in the {Betti} moduli of quasi-projective varieties},
  year = {2025},
  eprint = {2507.00167},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  note = {arXiv:2507.00167v1},
  url = {https://arxiv.org/abs/2507.00167v1}
}

@article{Mellit,
  author = {Mellit, Anton},
  title = {Toric stratifications of character varieties},
  journal = {Publ. Math. Inst. Hautes \'Etudes Sci.},
  volume = {142},
  year = {2025},
  pages = {153--240},
  doi = {10.1007/s10240-025-00158-0}
}

@article{Su,
  author = {Su, Tao},
  title = {Cell decomposition and dual boundary complexes of character varieties},
  journal = {Adv. Math.},
  volume = {498},
  year = {2026},
  pages = {111043},
  doi = {10.1016/j.aim.2026.111043},
  eprint = {2307.16657},
  archivePrefix = {arXiv}
}

@article{FranjouVanderKallen,
  author = {Franjou, Vincent and van der Kallen, Wilberd},
  title = {Power reductivity over an arbitrary base},
  journal = {Doc. Math.},
  year = {2010},
  volume = {Extra Volume: Andrei A. Suslin's Sixtieth Birthday},
  pages = {171--195},
  doi = {10.4171/DMS/5/5},
  url = {https://ems.press/books/dms/255/5058}
}

@incollection{MumfordSuominen,
  author = {Mumford, David and Suominen, Kalevi},
  title = {Introduction to the theory of moduli},
  booktitle = {Algebraic Geometry, Oslo 1970},
  editor = {Oort, Frans},
  publisher = {Wolters-Noordhoff},
  address = {Groningen},
  year = {1972},
  pages = {171--222},
  url = {https://www.dam.brown.edu/people/mumford/alg_geom/papers/1972d--IntroModuli-NC.pdf}
}

@article{BateMartinRoehrleTange,
  author = {Bate, Michael and Martin, Benjamin and R{\"o}hrle, Gerhard and Tange, Rudolf},
  title = {Complete reducibility and conjugacy classes of tuples in algebraic groups and {Lie} algebras},
  journal = {Math. Z.},
  volume = {269},
  year = {2011},
  pages = {809--832},
  doi = {10.1007/s00209-010-0763-9},
  eprint = {0905.0065},
  archivePrefix = {arXiv}
}

@article{Gerstenhaber1961,
  author = {Gerstenhaber, Murray},
  title = {On dominance and varieties of commuting matrices},
  journal = {Ann. of Math. (2)},
  volume = {73},
  year = {1961},
  pages = {324--348},
  doi = {10.2307/1970336}
}

@article{Guralnick1992,
  author = {Guralnick, Robert M.},
  title = {A note on commuting pairs of matrices},
  journal = {Linear Multilinear Algebra},
  volume = {31},
  year = {1992},
  pages = {71--75},
  doi = {10.1080/03081089208818123}
}

@article{LiebeckShalev2005,
  author = {Liebeck, Martin W. and Shalev, Aner},
  title = {{Fuchsian} groups, finite simple groups and representation varieties},
  journal = {Invent. Math.},
  volume = {159},
  year = {2005},
  pages = {317--367},
  doi = {10.1007/s00222-004-0390-3}
}

@article{LangWeil1954,
  author = {Lang, Serge and Weil, Andr{\'e}},
  title = {Number of points of varieties in finite fields},
  journal = {Amer. J. Math.},
  volume = {76},
  number = {4},
  year = {1954},
  pages = {819--827},
  doi = {10.2307/2372655}
}

@misc{MilneANT,
  author = {Milne, James S.},
  title = {Algebraic Number Theory},
  year = {2020},
  note = {Version 3.08},
  howpublished = {\url{https://www.jmilne.org/math/CourseNotes/ANTc.pdf}},
  url = {https://www.jmilne.org/math/CourseNotes/ANTc.pdf}
}

@misc{LittProblems,
  author = {Litt, Daniel},
  title = {Problems {I} {Like}, {Problem} 7},
  howpublished = {\url{https://www.problemsilike.com/7}},
  note = {Accessed 2 October 2026}
}

@misc{Litt2024,
  author = {Litt, Daniel},
  title = {Motives, mapping class groups, and monodromy},
  year = {2024},
  eprint = {2409.02234},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  note = {arXiv:2409.02234v1},
  url = {https://arxiv.org/abs/2409.02234v1}
}

@article{WhangDescent,
  author = {Whang, Junho Peter},
  title = {Nonlinear descent on moduli of local systems},
  journal = {Israel J. Math.},
  volume = {240},
  number = {2},
  year = {2020},
  pages = {935--1004},
  doi = {10.1007/s11856-020-2085-x},
  eprint = {1710.01848},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1710.01848v2}
}

@article{GhoshSarnak,
  author = {Ghosh, Amit and Sarnak, Peter},
  title = {Integral points on {Markoff} type cubic surfaces},
  journal = {Invent. Math.},
  volume = {229},
  number = {2},
  year = {2022},
  pages = {689--749},
  doi = {10.1007/s00222-022-01114-z},
  eprint = {1706.06712},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1706.06712}
}

@article{Goldman1986,
  author = {Goldman, William M.},
  title = {Invariant functions on {Lie} groups and {Hamiltonian} flows of surface group representations},
  journal = {Invent. Math.},
  volume = {85},
  number = {2},
  year = {1986},
  pages = {263--302},
  doi = {10.1007/BF01389091},
  url = {https://www.math.umd.edu/~wmg/InvariantFunctions.pdf}
}

@article{MotzkinTaussky1955,
  author = {Motzkin, T. S. and Taussky, Olga},
  title = {Pairs of matrices with property {L}. {II}},
  journal = {Trans. Amer. Math. Soc.},
  volume = {80},
  number = {2},
  year = {1955},
  pages = {387--401},
  doi = {10.1090/S0002-9947-1955-0086781-5}
}

@article{GuralnickSethuraman2000,
  author = {Guralnick, Robert M. and Sethuraman, B. A.},
  title = {Commuting pairs and triples of matrices and related varieties},
  journal = {Linear Algebra Appl.},
  volume = {310},
  number = {1--3},
  year = {2000},
  pages = {139--148},
  doi = {10.1016/S0024-3795(00)00065-3},
  url = {https://www.csun.edu/~asethura/papers/CommPairsTriples.pdf}
}

@book{Poonen2017,
  author = {Poonen, Bjorn},
  title = {Rational points on varieties},
  series = {Graduate Studies in Mathematics},
  volume = {186},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2017},
  doi = {10.1090/gsm/186},
  url = {https://math.mit.edu/~poonen/papers/Qpoints.pdf}
}

@article{Simpson1992,
  author = {Simpson, Carlos T.},
  title = {Higgs bundles and local systems},
  journal = {Publ. Math. Inst. Hautes \'Etudes Sci.},
  volume = {75},
  year = {1992},
  pages = {5--95},
  doi = {10.1007/BF02699491}
}

@article{EsnaultGroechenig2018,
  author = {Esnault, H{\'e}l{\`e}ne and Groechenig, Michael},
  title = {Cohomologically rigid local systems and integrality},
  journal = {Selecta Math. (N.S.)},
  volume = {24},
  number = {5},
  year = {2018},
  pages = {4279--4292},
  doi = {10.1007/s00029-018-0409-z}
}

@article{DeJongEsnault2024,
  author = {de Jong, Johan and Esnault, H{\'e}l{\`e}ne},
  title = {Integrality of the {Betti} moduli space},
  journal = {Trans. Amer. Math. Soc.},
  volume = {377},
  number = {1},
  year = {2024},
  pages = {431--448},
  doi = {10.1090/tran/8928}
}
