@misc{soule_abc,
  author        = {Soul{\'e}, Christophe},
  title         = {On the $abc$ conjecture},
  year          = {2026},
  eprint        = {2611.05217},
  archiveprefix = {arXiv},
  primaryclass  = {math.NT},
  note          = {v1, 3 November 2026. Theorem A, Theorem B, \S7.2.
                   Statement and scope verified verbatim; internal proof
                   NOT independently verified (see Appendix G of the
                   companion audit)}
}

@misc{soule_ihes,
  author = {Soul{\'e}, Christophe},
  title  = {On the {A}rakelov theory of arithmetic surfaces},
  year   = {2017},
  note   = {IH{\'E}S lecture notes, Lecture 3: the $5$-fold root cover,
            $\frac54\cdot\frac45=1$}
}

@article{soule_drr,
  author   = {Soul{\'e}, Christophe},
  title    = {Secant varieties and successive minima},
  journal  = {Journal of Algebraic Geometry},
  volume   = {13},
  number   = {2},
  year     = {2004},
  pages    = {323--341},
  mrnumber = {2047701},
  eprint   = {math/0110254},
  archiveprefix = {arXiv}
}

@misc{soule_vs,
  author        = {Soul{\'e}, Christophe},
  title         = {Very stable extensions on arithmetic surfaces},
  year          = {2010},
  eprint        = {1009.6191},
  archiveprefix = {arXiv}
}

@misc{soule_ss,
  author        = {Soul{\'e}, Christophe},
  title         = {Semi-stable extensions on arithmetic surfaces},
  year          = {2005},
  eprint        = {math/0505079},
  archiveprefix = {arXiv}
}

@misc{moret_bailly_formule_clef,
  author = {Moret-Bailly, Laurent},
  title  = {La formule clef},
  note   = {For abelian schemes; cf.\ ref.~16 of arXiv:2611.05217}
}

@incollection{deligne_determinant,
  author    = {Deligne, Pierre},
  title     = {Le d{\'e}terminant de la cohomologie},
  booktitle = {Current Trends in Arithmetical Algebraic Geometry},
  series    = {Contemporary Mathematics},
  volume    = {67},
  publisher = {American Mathematical Society},
  address   = {Providence, RI},
  year      = {1987},
  pages     = {93--177},
  mrnumber  = {0902592}
}

@article{faltings_calculus,
  author   = {Faltings, Gerd},
  title    = {Calculus on arithmetic surfaces},
  journal  = {Annals of Mathematics (2)},
  volume   = {119},
  number   = {2},
  year     = {1984},
  pages    = {387--424},
  mrnumber = {0740897}
}

@article{gillet_soule_arithmetic_rr,
  author   = {Gillet, Henri and Soul{\'e}, Christophe},
  title    = {An arithmetic {R}iemann--{R}och theorem},
  journal  = {Inventiones Mathematicae},
  volume   = {110},
  number   = {3},
  year     = {1992},
  pages    = {473--543},
  mrnumber = {1189489}
}

@book{vojta_da_vdt,
  author    = {Vojta, Paul},
  title     = {Diophantine Approximations and Value Distribution Theory},
  series    = {Lecture Notes in Mathematics},
  volume    = {1239},
  publisher = {Springer-Verlag},
  address   = {Berlin},
  year      = {1987}
}

@misc{masser_oesterle,
  author = {Masser, D. W. and Oesterl{\'e}, J.},
  title  = {The $abc$ conjecture},
  year   = {1985},
  note   = {Formulation 1985/1988; cf.\ \S1 of arXiv:2611.05217}
}

@article{szpiro_discriminant,
  author  = {Szpiro, Lucien},
  title   = {Discriminant et conducteur des courbes elliptiques},
  journal = {Ast{\'e}risque},
  volume  = {183},
  year    = {1990},
  note    = {Cf.\ \S1 of arXiv:2611.05217}
}

@article{frey_links,
  author  = {Frey, Gerhard},
  title   = {Links between stable elliptic curves and certain {D}iophantine
             equations},
  journal = {Annales Universitatis Saraviensis, Series Mathematicae},
  volume  = {1},
  year    = {1986},
  pages   = {1--40}
}

@misc{parshin_fibrations,
  author = {Parshin, A. N.},
  title  = {Fibrations of algebraic curves and the {M}ordell conjecture},
  note   = {Cf.\ \S3 of arXiv:2611.05217}
}

@article{arakelov_intersection,
  author   = {Arakelov, S. Yu.},
  title    = {Intersection theory of divisors on an arithmetic surface},
  journal  = {Mathematics of the USSR-Izvestiya},
  volume   = {8},
  year     = {1974},
  pages    = {1167--1180},
  mrnumber = {0472815}
}

@book{mason_function_fields,
  author    = {Mason, R. C.},
  title     = {Diophantine Equations over Function Fields},
  series    = {London Mathematical Society Lecture Note Series},
  volume    = {96},
  publisher = {Cambridge University Press},
  year      = {1984},
  note      = {See also W. D. Stothers (1981)}
}

@misc{buium_omega,
  author = {Buium, Alexandru},
  title  = {Arithmetic differential operators and
            $\Omega^{1}_{\mathbb{Z}}=0$},
  note   = {Cf.\ arXiv:2611.05217}
}

@article{greenberg_stevens,
  author   = {Greenberg, Ralph and Stevens, Glenn},
  title    = {$p$-adic {$L$}-functions and $p$-adic periods of modular forms},
  journal  = {Inventiones Mathematicae},
  volume   = {111},
  number   = {2},
  year     = {1993},
  pages    = {407--447},
  mrnumber = {1198816}
}

@misc{eriksson_freixas_drr,
  author        = {Eriksson, Dennis and Freixas i Montplet, Gerard},
  title         = {Arithmetic {D}eligne--{R}iemann--{R}och},
  year          = {2025},
  eprint        = {2509.05077},
  archiveprefix = {arXiv},
  note          = {See also D. V. Osipov, Izv.\ Math.\ 88(5), 2024}
}

@article{pasten_shimura_curves,
  author  = {Pasten, Hector},
  title   = {Shimura curves and the $abc$ conjecture},
  journal = {Journal of Number Theory},
  volume  = {254},
  year    = {2024},
  pages   = {214--335},
  eprint  = {1705.09251},
  archiveprefix = {arXiv}
}

@misc{pasten_szpiro,
  author        = {Pasten, Hector},
  title         = {Improved bounds for {S}zpiro's conjecture},
  year          = {2026},
  eprint        = {2609.17390},
  archiveprefix = {arXiv},
  note          = {v1, 15 September 2026}
}

@misc{laniewski_mueller_quality,
  author        = {Laniewski, R. and M{\"u}ller, K.},
  title         = {The quality plane of $abc$-triples and the
                   decomposition into gains},
  year          = {2026},
  eprint        = {2610.03212},
  archiveprefix = {arXiv},
  note          = {v1, 2 October 2026}
}

@article{ballay_slopes,
  author   = {Ballay, Fran{\c c}ois},
  title    = {Successive minima and asymptotic slopes in {A}rakelov geometry},
  journal  = {Compositio Mathematica},
  volume   = {157},
  number   = {6},
  year     = {2021},
  pages    = {1302--1339},
  eprint   = {2002.06026},
  archiveprefix = {arXiv}
}

@article{zhang_admissible,
  author   = {Zhang, Shou-Wu},
  title    = {Admissible pairing on a curve},
  journal  = {Inventiones Mathematicae},
  volume   = {112},
  number   = {1},
  year     = {1993},
  pages    = {171--193},
  mrnumber = {1207481}
}

@article{bombieri_vaaler_siegel,
  author   = {Bombieri, Enrico and Vaaler, Jeffrey D.},
  title    = {On {S}iegel's lemma},
  journal  = {Inventiones Mathematicae},
  volume   = {73},
  year     = {1983},
  pages    = {11--32},
  mrnumber = {0707346},
  note     = {Addendum: ibid.\ 75 (1984), 377}
}

@article{borek_slopes,
  author  = {Borek, Thomas},
  title   = {Successive minima and slopes of {H}ermitian vector bundles
             over number fields},
  journal = {Journal of Number Theory},
  volume  = {113},
  number  = {2},
  year    = {2005},
  pages   = {380--388}
}

@article{zhang_small_points,
  author   = {Zhang, Shou-Wu},
  title    = {Small points and adelic metrics},
  journal  = {Journal of Algebraic Geometry},
  volume   = {4},
  number   = {2},
  year     = {1995},
  pages    = {281--300},
  mrnumber = {1311351}
}

@misc{yuan_zhang_adelic,
  author        = {Yuan, Xinyi and Zhang, Shou-Wu},
  title         = {Adelic line bundles on quasi-projective varieties},
  year          = {2021},
  eprint        = {2105.13587},
  archiveprefix = {arXiv},
  note          = {to appear in Annals of Mathematics Studies}
}

@misc{moriwaki_adelic,
  author = {Moriwaki, Atsushi},
  title  = {Adelic sequences and adelic structures over finitely generated
           fields},
  year   = {1999},
  note   = {Kyoto Univ.\ preprint 1999-19}
}

@article{gaudron_siegel,
  author  = {Gaudron, {\'E}ric},
  title   = {G{\'e}om{\'e}trie des nombres ad{\'e}lique et lemmes de
             {S}iegel g{\'e}n{\'e}ralis{\'e}s},
  journal = {Manuscripta Mathematica},
  volume  = {130},
  number  = {2},
  year    = {2009},
  pages   = {159--182}
}

@article{gillet_rossler_soule_higher,
  author   = {Gillet, Henri and R{\"o}ssler, Damian and Soul{\'e}, Christophe},
  title    = {An arithmetic {R}iemann--{R}och theorem in higher degrees},
  journal  = {Annales de l'Institut Fourier (Grenoble)},
  volume   = {58},
  number   = {6},
  year     = {2008},
  pages    = {2169--2189},
  mrnumber = {2473633}
}

@book{faltings_lectures,
  author    = {Faltings, Gerd},
  title     = {Lectures on the Arithmetic {R}iemann--{R}och Theorem},
  series    = {Annals of Mathematics Studies},
  volume    = {127},
  publisher = {Princeton University Press},
  address   = {Princeton, NJ},
  year      = {1992},
  note      = {Notes taken by Shou-Wu Zhang},
  mrnumber  = {1158661}
}

@article{stewart_yu_1,
  author  = {Stewart, Cameron L. and Yu, Kunrui},
  title   = {On the {$abc$} conjecture},
  journal = {Mathematische Annalen},
  volume  = {321},
  year    = {2001},
  pages   = {705--726}
}

@article{stewart_yu_2,
  author  = {Stewart, Cameron L. and Yu, Kunrui},
  title   = {On the {$abc$} conjecture, {II}},
  journal = {Duke Mathematical Journal},
  volume  = {108},
  year    = {2001},
  pages   = {169--181}
}

@article{stewart_tijdeman,
  author  = {Stewart, Cameron L. and Tijdeman, Robert},
  title   = {On the {$abc$}-conjecture},
  journal = {Monatshefte f{\"u}r Mathematik},
  volume  = {102},
  year    = {1986},
  pages   = {251--257}
}

@article{moret_bailly_1990,
  author  = {Moret-Bailly, Laurent},
  title   = {Hauteurs et classes de {C}hern sur les surfaces
             arithm{\'e}tiques},
  journal = {Ast{\'e}risque},
  volume  = {183},
  year    = {1990},
  pages   = {37--58}
}

@book{bombieri_gubler,
  author    = {Bombieri, Enrico and Gubler, Walter},
  title     = {Heights in Diophantine Geometry},
  publisher = {Cambridge University Press},
  series    = {New Mathematical Monographs},
  volume    = {4},
  year      = {2006}
}

@book{neukirch,
  author    = {Neukirch, J{\"u}rgen},
  title     = {Algebraic Number Theory},
  publisher = {Springer-Verlag},
  year      = {1999},
  note      = {Chap.~III, \S2, Th.~2.11 (translative discriminant formula)}
}

@article{zhang_positive,
  author  = {Zhang, Shou-Wu},
  title   = {Positive line bundles on arithmetic varieties},
  journal = {Journal of the American Mathematical Society},
  volume  = {8},
  year    = {1995},
  pages   = {187--221}
}

@article{van_frankenhuysen,
  author  = {van Frankenhuysen, Machiel},
  title   = {The {$ABC$} conjecture implies {V}ojta's height inequality
             on the complement of a degree four divisor in {$\mathbb{P}^2$}},
  journal = {Journal of Number Theory},
  volume  = {95},
  year    = {2002},
  pages   = {289--302}
}