@book{AMRT,
  author    = {Ash, Avner and Mumford, David and Rapoport, Michael and Tai, Yung-Sheng},
  title     = {Smooth Compactifications of Locally Symmetric Varieties},
  edition   = {Second},
  series    = {Cambridge Mathematical Library},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2010},
  note      = {\DOI{10.1017/CBO9780511674693}}
}

@article{AmorosoDvornicich,
  author  = {Amoroso, Francesco and Dvornicich, Roberto},
  title   = {Lower bounds for the height and size of the ideal class group in {CM}-fields},
  journal = {Monatsh. Math.},
  volume  = {138},
  number  = {2},
  year    = {2003},
  pages   = {85--94},
  note    = {\DOI{10.1007/s00605-002-0499-7}}
}

@article{Andre92,
  author  = {Andr\'e, Yves},
  title   = {Mumford--{T}ate groups of mixed {H}odge structures and the theorem of the fixed part},
  journal = {Compositio Math.},
  volume  = {82},
  number  = {1},
  year    = {1992},
  pages   = {1--24}
}

@article{BSY,
  author  = {Binyamini, Gal and Schmidt, Harry and Yafaev, Andrei},
  title   = {Lower bounds for {G}alois orbits of special points on {S}himura varieties: a point-counting approach},
  journal = {Math. Ann.},
  volume  = {385},
  number  = {1-2},
  year    = {2023},
  pages   = {961--973},
  note    = {\DOI{10.1007/s00208-021-02309-0}, \arXiv{2104.05842}}
}

@article{BJST,
  author  = {Binyamini, Gal and Jones, Gareth O. and Schmidt, Harry and Thomas, Margaret E. M.},
  title   = {An effective {P}ila--{W}ilkie theorem for sets definable using {P}faffian functions, with some diophantine applications},
  journal = {J. Eur. Math. Soc. (JEMS)},
  year    = {2026},
  note    = {Published online first, \DOI{10.4171/JEMS/1761}, \arXiv{2301.09883v1}; theorem numbers refer to v1}
}

@article{BMZ,
  author  = {Bilu, Yuri and Masser, David and Zannier, Umberto},
  title   = {An effective ``theorem of {A}ndr\'e'' for {CM}-points on a plane curve},
  journal = {Math. Proc. Cambridge Philos. Soc.},
  volume  = {154},
  number  = {1},
  year    = {2013},
  pages   = {145--152}
}

@article{BinyaminiCrelle,
  author  = {Binyamini, Gal},
  title   = {Some effective estimates for {A}ndr\'e--{O}ort in {$Y(1)^n$}},
  journal = {J. Reine Angew. Math.},
  volume  = {767},
  year    = {2020},
  pages   = {17--35},
  note    = {With an appendix by Emmanuel Kowalski, \DOI{10.1515/crelle-2019-0028}, \arXiv{1809.05302}}
}

@article{BinyaminiMasser,
  author  = {Binyamini, Gal and Masser, David},
  title   = {Effective {A}ndr\'e--{O}ort for non-compact curves in {H}ilbert modular varieties},
  journal = {C. R. Math. Acad. Sci. Paris},
  volume  = {359},
  year    = {2021},
  pages   = {313--321},
  note    = {\arXiv{2101.06412}}
}

@article{ClozelUllmo,
  author  = {Clozel, Laurent and Ullmo, Emmanuel},
  title   = {\'{E}quidistribution de sous-vari\'et\'es sp\'eciales},
  journal = {Ann. of Math. (2)},
  volume  = {161},
  number  = {3},
  year    = {2005},
  pages   = {1571--1588},
  note    = {\DOI{10.4007/annals.2005.161.1571}}
}

@incollection{Conrad,
  author    = {Conrad, Brian},
  title     = {Reductive group schemes},
  booktitle = {Autour des sch\'emas en groupes. {V}ol. {I}},
  series    = {Panor. Synth\`eses},
  volume    = {42/43},
  publisher = {Soc. Math. France},
  address   = {Paris},
  year      = {2014},
  pages     = {93--444}
}

@misc{CTLean,
  author = {{AxiomMath}},
  title  = {{DedekindZetaZeroFree}: a {L}ean formalization of a zero-free half-plane for {D}edekind zeta functions},
  year   = {2026},
  note   = {\url{https://github.com/AxiomMath/DedekindZetaZeroFree}, commit 09afbb4c}
}

@misc{CuretonThorner,
  author = {Cureton, Dean and Thorner, Jesse},
  title  = {A quasi-{R}iemann hypothesis for {D}edekind zeta functions},
  year   = {2026},
  note   = {Preprint, Hexagon 2610.00200v2, \url{https://hexagonmath.org/2610.00200v2}}
}

@misc{DKN,
  author = {Das, Sourabhashis and Kadiri, Habiba and Ng, Nathan},
  title  = {An effective version of {C}hebotarev's density theorem},
  year   = {2025},
  note   = {Preprint, \arXiv{2508.09480v1}}
}

@article{Daw,
  author  = {Daw, Christopher},
  title   = {Degrees of strongly special subvarieties and the {A}ndr\'e--{O}ort conjecture},
  journal = {J. Reine Angew. Math.},
  volume  = {721},
  year    = {2016},
  pages   = {81--108},
  note    = {\DOI{10.1515/crelle-2014-0062}}
}

@article{DawOrr,
  author  = {Daw, Christopher and Orr, Martin},
  title   = {Heights of pre-special points of {S}himura varieties},
  journal = {Math. Ann.},
  volume  = {365},
  number  = {3-4},
  year    = {2016},
  pages   = {1305--1357},
  note    = {\DOI{10.1007/s00208-015-1328-3}, \arXiv{1502.00822v5}; we cite the numbering of the arXiv version}
}

@article{DiCerbo,
  author  = {Di Cerbo, Gabriele and Di Cerbo, Luca F.},
  title   = {Effective results for complex hyperbolic manifolds},
  journal = {J. Lond. Math. Soc. (2)},
  volume  = {91},
  number  = {1},
  year    = {2015},
  pages   = {89--104},
  note    = {\DOI{10.1112/jlms/jdu065}, \arXiv{1212.0501v5}; corollary numbers refer to v5}
}

@article{DJK,
  author  = {Daw, Christopher and Javanpeykar, Ariyan and K\"uhne, Lars},
  title   = {Effective estimates for the degrees of maximal special subvarieties},
  journal = {Selecta Math. (N.S.)},
  volume  = {26},
  number  = {1},
  year    = {2020},
  pages   = {Paper No.~2},
  note    = {\DOI{10.1007/s00029-019-0528-1}, \arXiv{1812.04341v2}; page numbers refer to v2}
}

@incollection{Edixhoven,
  author    = {Edixhoven, Bas},
  title     = {On the {A}ndr\'e--{O}ort conjecture for {H}ilbert modular surfaces},
  booktitle = {Moduli of Abelian Varieties ({T}exel {I}sland, 1999)},
  series    = {Progr. Math.},
  volume    = {195},
  publisher = {Birkh\"auser},
  address   = {Basel},
  year      = {2001},
  pages     = {133--155},
  note      = {\arXiv{math/9911272}}
}

@article{EY,
  author  = {Edixhoven, Bas and Yafaev, Andrei},
  title   = {Subvarieties of {S}himura varieties},
  journal = {Ann. of Math. (2)},
  volume  = {157},
  number  = {2},
  year    = {2003},
  pages   = {621--645},
  note    = {\arXiv{math/0105241}}
}

@article{Fowler24,
  author  = {Fowler, Guy},
  title   = {Some uniform effective results on {A}ndr\'e--{O}ort for sums of powers in {$\mathbb{C}^n$}},
  journal = {Math. Proc. Cambridge Philos. Soc.},
  volume  = {180},
  number  = {3},
  year    = {2026},
  pages   = {607--641},
  note    = {\DOI{10.1017/S0305004125101825}, \arXiv{2405.06456}}
}

@misc{Fowler26,
  author = {Fowler, Guy},
  title  = {A uniform effective {A}ndr\'e--{O}ort result},
  year   = {2026},
  note   = {Preprint, \arXiv{2609.18934}}
}

@article{Fujino,
  author  = {Fujino, Osamu},
  title   = {Effective base point free theorem for log canonical pairs {II}. {A}ngehrn--{S}iu type theorems},
  journal = {Michigan Math. J.},
  volume  = {59},
  number  = {2},
  year    = {2010},
  pages   = {303--312},
  note    = {\arXiv{0709.0336}}
}

@incollection{FultonLazarsfeld,
  author    = {Fulton, William and Lazarsfeld, Robert},
  title     = {Positivity and excess intersection},
  booktitle = {Enumerative Geometry and Classical Algebraic Geometry ({N}ice, 1981)},
  series    = {Progr. Math.},
  volume    = {24},
  publisher = {Birkh\"auser},
  address   = {Boston, MA},
  year      = {1982},
  pages     = {97--105}
}

@book{Fulton,
  author    = {Fulton, William},
  title     = {Intersection Theory},
  edition   = {Second},
  series    = {Ergeb. Math. Grenzgeb. (3)},
  volume    = {2},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1998}
}

@misc{Hu,
  author = {Hu, Boyang},
  title  = {A seven-eighths zero-free half-plane for unitary {W}eil {$L$}-functions},
  year   = {2026},
  note   = {Preprint, Hexagon 2610.00216v2, \url{https://hexagonmath.org/2610.00216v2}; Lean formalization \url{https://github.com/Rogerhu12/hecke-seven-eighths}, commit c77efa92}
}

@incollection{HulekSankaran,
  author    = {Hulek, Klaus and Sankaran, Gregory K.},
  title     = {The geometry of {S}iegel modular varieties},
  booktitle = {Higher Dimensional Birational Geometry ({K}yoto, 1997)},
  series    = {Adv. Stud. Pure Math.},
  volume    = {35},
  publisher = {Math. Soc. Japan},
  address   = {Tokyo},
  year      = {2002},
  pages     = {89--156},
  note      = {\arXiv{math/9810153}}
}

@article{KY,
  author  = {Klingler, Bruno and Yafaev, Andrei},
  title   = {The {A}ndr\'e--{O}ort conjecture},
  journal = {Ann. of Math. (2)},
  volume  = {180},
  number  = {3},
  year    = {2014},
  pages   = {867--925},
  note    = {\DOI{10.4007/annals.2014.180.3.2}, \arXiv{1209.0936v2}; page numbers refer to v2}
}

@incollection{Kollar,
  author    = {Koll\'ar, J\'anos},
  title     = {Singularities of pairs},
  booktitle = {Algebraic Geometry---{S}anta {C}ruz 1995},
  series    = {Proc. Sympos. Pure Math.},
  volume    = {62, Part 1},
  publisher = {Amer. Math. Soc.},
  address   = {Providence, RI},
  year      = {1997},
  pages     = {221--287}
}

@article{Kuhne,
  author  = {K\"uhne, Lars},
  title   = {An effective result of {A}ndr\'e--{O}ort type},
  journal = {Ann. of Math. (2)},
  volume  = {176},
  number  = {1},
  year    = {2012},
  pages   = {651--671}
}

@incollection{LO,
  author    = {Lagarias, Jeffrey C. and Odlyzko, Andrew M.},
  title     = {Effective versions of the {C}hebotarev density theorem},
  booktitle = {Algebraic Number Fields: {$L$}-Functions and {G}alois Properties ({D}urham, 1975)},
  publisher = {Academic Press},
  address   = {London},
  year      = {1977},
  pages     = {409--464}
}

@book{MalleTesterman,
  author    = {Malle, Gunter and Testerman, Donna},
  title     = {Linear Algebraic Groups and Finite Groups of {L}ie Type},
  series    = {Cambridge Stud. Adv. Math.},
  volume    = {133},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2011}
}

@incollection{Milne,
  author    = {Milne, James S.},
  title     = {Introduction to {S}himura varieties},
  booktitle = {Harmonic Analysis, the Trace Formula, and {S}himura Varieties},
  series    = {Clay Math. Proc.},
  volume    = {4},
  publisher = {Amer. Math. Soc.},
  address   = {Providence, RI},
  year      = {2005},
  note      = {pp.~265--378; revised version (2017) at \url{https://www.jmilne.org/math/xnotes/svi.pdf}, whose display, footnote and page numbers we cite}
}

@article{Mumford77,
  author  = {Mumford, David},
  title   = {Hirzebruch's proportionality theorem in the non-compact case},
  journal = {Invent. Math.},
  volume  = {42},
  year    = {1977},
  pages   = {239--272}
}

@article{PilaWilkie,
  author  = {Pila, Jonathan and Wilkie, Alex J.},
  title   = {The rational points of a definable set},
  journal = {Duke Math. J.},
  volume  = {133},
  number  = {3},
  year    = {2006},
  pages   = {591--616}
}

@article{PilaZannier,
  author  = {Pila, Jonathan and Zannier, Umberto},
  title   = {Rational points in periodic analytic sets and the {M}anin--{M}umford conjecture},
  journal = {Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. (9)},
  volume  = {19},
  number  = {2},
  year    = {2008},
  pages   = {149--162}
}

@article{Papas,
  author  = {Papas, Georgios},
  title   = {Effective {B}rauer--{S}iegel on some curves in {$Y(1)^n$}},
  journal = {Math. Ann.},
  volume  = {394},
  year    = {2026},
  pages   = {Paper No.~84},
  note    = {\arXiv{2310.04943}}
}

@misc{PST,
  author = {Pila, Jonathan and Shankar, Ananth N. and Tsimerman, Jacob},
  title  = {Canonical heights on {S}himura varieties and the {A}ndr\'e--{O}ort conjecture},
  year   = {2021},
  note   = {With an appendix by H\'el\`ene Esnault and Michael Groechenig. Preprint, \arXiv{2109.08788v4}}
}

@book{Pink,
  author    = {Pink, Richard},
  title     = {Arithmetical Compactification of Mixed {S}himura Varieties},
  series    = {Bonner Math. Schriften},
  volume    = {209},
  publisher = {Universit\"at Bonn, Mathematisches Institut},
  address   = {Bonn},
  year      = {1990},
  note      = {Dissertation, Bonn 1989}
}

@article{RosserSchoenfeld,
  author  = {Rosser, J. Barkley and Schoenfeld, Lowell},
  title   = {Approximate formulas for some functions of prime numbers},
  journal = {Illinois J. Math.},
  volume  = {6},
  year    = {1962},
  pages   = {64--94}
}

@misc{Stacks,
  author = {{The Stacks project authors}},
  title  = {The {S}tacks project},
  year   = {2026},
  note   = {\url{https://stacks.math.columbia.edu}}
}

@article{Stark,
  author  = {Stark, Harold M.},
  title   = {Some effective cases of the {B}rauer--{S}iegel theorem},
  journal = {Invent. Math.},
  volume  = {23},
  year    = {1974},
  pages   = {135--152}
}

@article{Tsimerman12,
  author  = {Tsimerman, Jacob},
  title   = {Brauer--{S}iegel for arithmetic tori and lower bounds for {G}alois orbits of special points},
  journal = {J. Amer. Math. Soc.},
  volume  = {25},
  number  = {4},
  year    = {2012},
  pages   = {1091--1117},
  note    = {\DOI{10.1090/S0894-0347-2012-00739-5}, \arXiv{1103.5619v3}; we cite the numbering of the arXiv version}
}

@article{Tsimerman,
  author  = {Tsimerman, Jacob},
  title   = {The {A}ndr\'e--{O}ort conjecture for {$\mathcal{A}_g$}},
  journal = {Ann. of Math. (2)},
  volume  = {187},
  number  = {2},
  year    = {2018},
  pages   = {379--390},
  note    = {\arXiv{1506.01466v5}; corollary numbers refer to v5}
}

@article{Ullmo07,
  author  = {Ullmo, Emmanuel},
  title   = {\'{E}quidistribution de sous-vari\'et\'es sp\'eciales. {II}},
  journal = {J. Reine Angew. Math.},
  volume  = {606},
  year    = {2007},
  pages   = {193--216}
}

@article{UY,
  author  = {Ullmo, Emmanuel and Yafaev, Andrei},
  title   = {Galois orbits and equidistribution of special subvarieties: towards the {A}ndr\'e--{O}ort conjecture},
  journal = {Ann. of Math. (2)},
  volume  = {180},
  number  = {3},
  year    = {2014},
  pages   = {823--865},
  note    = {\DOI{10.4007/annals.2014.180.3.1}, \arXiv{1209.0934v2}; page numbers refer to v2}
}

@article{UY15,
  author  = {Ullmo, Emmanuel and Yafaev, Andrei},
  title   = {Nombre de classes des tores de multiplication complexe et bornes inf\'erieures pour les orbites galoisiennes de points sp\'eciaux},
  journal = {Bull. Soc. Math. France},
  volume  = {143},
  number  = {1},
  year    = {2015},
  pages   = {197--228},
  note    = {\arXiv{1209.0942v2}; page numbers refer to v2}
}

@article{Yafaev,
  author  = {Yafaev, Andrei},
  title   = {A conjecture of {Y}ves {A}ndr\'e's},
  journal = {Duke Math. J.},
  volume  = {132},
  number  = {3},
  year    = {2006},
  pages   = {393--407},
  note    = {\arXiv{math/0302125v1}; we cite the numbering of the arXiv version}
}

@misc{Record,
  author = {Jaswal, Manvir},
  title  = {Programs and data for ``{An} effective {A}ndr\'e--{O}ort theorem for {S}himura varieties''},
  year   = {2026},
  note   = {Zenodo, \DOI{10.5281/zenodo.24136430}}
}

@article{BLH,
  author  = {Barakat, Mohamed and Lange-Hegermann, Markus},
  title   = {An algorithmic approach to {C}hevalley's theorem on images of rational morphisms between affine varieties},
  journal = {Math. Comp.},
  volume  = {91},
  number  = {333},
  year    = {2022},
  pages   = {451--490},
  note    = {\DOI{10.1090/mcom/3632}, \arXiv{1911.10411v3}}
}

@article{EGAII,
  author  = {Grothendieck, Alexander},
  title   = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {II}. \'{E}tude globale \'el\'ementaire de quelques classes de morphismes},
  journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  volume  = {8},
  year    = {1961},
  pages   = {5--222}
}

@article{EGAIV4,
  author  = {Grothendieck, Alexander},
  title   = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {IV}. \'{E}tude locale des sch\'emas et des morphismes de sch\'emas. {IV}},
  journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  volume  = {32},
  year    = {1967},
  pages   = {5--361}
}

@book{FaltingsChai,
  author    = {Faltings, Gerd and Chai, Ching-Li},
  title     = {Degeneration of Abelian Varieties},
  series    = {Ergeb. Math. Grenzgeb. (3)},
  volume    = {22},
  publisher = {Springer},
  address   = {Berlin},
  year      = {1990}
}

@article{Feng,
  author  = {Feng, Ruyong},
  title   = {Hrushovski's algorithm for computing the {G}alois group of a linear differential equation},
  journal = {Adv. in Appl. Math.},
  volume  = {65},
  year    = {2015},
  pages   = {1--37},
  note    = {\arXiv{1312.5029v3}}
}

@article{GLS,
  author  = {Greuel, Gert-Martin and Laplagne, Santiago and Seelisch, Frank},
  title   = {Normalization of rings},
  journal = {J. Symbolic Comput.},
  volume  = {45},
  year    = {2010},
  pages   = {887--901},
  note    = {\arXiv{0904.3561v3}}
}

@article{HammLe,
  author  = {Hamm, Helmut A. and {L\^e D\~{u}ng Tr\'ang}},
  title   = {Lefschetz theorems on quasi-projective varieties},
  journal = {Bull. Soc. Math. France},
  volume  = {113},
  year    = {1985},
  pages   = {123--142}
}

@book{Hartshorne,
  author    = {Hartshorne, Robin},
  title     = {Algebraic Geometry},
  series    = {Grad. Texts in Math.},
  volume    = {52},
  publisher = {Springer},
  address   = {New York},
  year      = {1977}
}

@article{Katz70,
  author  = {Katz, Nicholas M.},
  title   = {Nilpotent connections and the monodromy theorem: applications of a result of {T}urrittin},
  journal = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  volume  = {39},
  year    = {1970},
  pages   = {175--232}
}

@misc{Lella,
  author  = {Lella, Paolo},
  title   = {Computable {H}ilbert schemes},
  year    = {2012},
  note    = {PhD thesis, Universit\`a di Torino; \arXiv{1202.4384v1}}
}

@misc{MilneANT,
  author  = {Milne, James S.},
  title   = {Algebraic Number Theory},
  year    = {2020},
  note    = {Course notes, v3.08, \url{https://www.jmilne.org/math/}}
}

@misc{MilneAV,
  author  = {Milne, James S.},
  title   = {Abelian Varieties},
  year    = {2008},
  note    = {Course notes, v2.00, \url{https://www.jmilne.org/math/}}
}

@misc{MilneCFT,
  author  = {Milne, James S.},
  title   = {Class Field Theory},
  year    = {2020},
  note    = {Course notes, v4.03, \url{https://www.jmilne.org/math/}}
}

@article{MumfordI,
  author  = {Mumford, David},
  title   = {On the equations defining abelian varieties. {I}},
  journal = {Invent. Math.},
  volume  = {1},
  year    = {1966},
  pages   = {287--354}
}

@article{MumfordII,
  author  = {Mumford, David},
  title   = {On the equations defining abelian varieties. {II}},
  journal = {Invent. Math.},
  volume  = {3},
  year    = {1967},
  pages   = {75--135}
}

@article{Polishchuk,
  author  = {Polishchuk, Alexander},
  title   = {Determinant bundles for abelian schemes},
  journal = {Compositio Math.},
  volume  = {121},
  number  = {3},
  year    = {2000},
  pages   = {221--245},
  note    = {\DOI{10.1023/A:1001896315311}, \arXiv{alg-geom/9703021v2}}
}

@incollection{Singer,
  author    = {Singer, Michael F.},
  title     = {{G}alois theory of linear differential equations},
  booktitle = {Algebraic Theory of Differential Equations},
  series    = {London Math. Soc. Lecture Note Ser.},
  volume    = {357},
  publisher = {Cambridge Univ. Press},
  address   = {Cambridge},
  year      = {2009},
  pages     = {1--82},
  note      = {\DOI{10.1017/CBO9780511721564.002}, \arXiv{0712.4124v2}}
}

@book{Taylor,
  author    = {Taylor, Donald E.},
  title     = {The Geometry of the Classical Groups},
  series    = {Sigma Ser. Pure Math.},
  volume    = {9},
  publisher = {Heldermann},
  address   = {Berlin},
  year      = {1992}
}

@article{Urbanik,
  author  = {Urbanik, David},
  title   = {Sets of special subvarieties of bounded degree},
  journal = {Compositio Math.},
  volume  = {159},
  number  = {3},
  year    = {2023},
  pages   = {616--657},
  note    = {\DOI{10.1112/S0010437X23007029}, \arXiv{2109.07663v1}; we cite the numbering of v1}
}

@incollection{Deligne79,
  author    = {Deligne, Pierre},
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