@article{xu2024,
  author = {Xu, Zheng},
  title = {Note on the Three-Dimensional Log Canonical Abundance in Characteristic {$>3$}},
  journal = {Nagoya Mathematical Journal},
  volume = {255},
  year = {2024},
  pages = {694--723},
  doi = {10.1017/nmj.2024.3},
  eprint = {2212.04039},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/html/2212.04039v2},
  note = {Theorem numbering checked in arXiv version 2, 3 February 2024}
}

@misc{xu2026,
  author = {Xu, Zheng},
  title = {Abundance for Threefolds in Positive Characteristic When {$\nu=2$}},
  year = {2026},
  eprint = {2307.03938},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/html/2307.03938v3},
  note = {Version 3, 17 April 2026; first posted in 2023}
}

@article{posva2024,
  author = {Posva, Quentin},
  title = {Abundance for slc Surfaces over Arbitrary Fields},
  journal = {\'{E}pijournal de G\'{e}om\'{e}trie Alg\'{e}brique},
  volume = {7},
  year = {2023},
  pages = {1--23},
  doi = {10.46298/epiga.2023.volume7.8803},
  eprint = {2110.10543},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://epiga.episciences.org/10961},
  note = {Article no. 5; arXiv version 4, 13 February 2023}
}

@article{haconxu2015,
  author = {Hacon, Christopher D. and Xu, Chenyang},
  title = {On the Three Dimensional Minimal Model Program in Positive Characteristic},
  journal = {Journal of the American Mathematical Society},
  volume = {28},
  year = {2015},
  pages = {711--744},
  doi = {10.1090/S0894-0347-2014-00809-2},
  eprint = {1302.0298},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/html/1302.0298v2},
  note = {Theorem numbering checked in arXiv version 2, 27 June 2013}
}

@article{birkar2016,
  author = {Birkar, Caucher},
  title = {Existence of Flips and Minimal Models for {$3$}-folds in Characteristic {$p$}},
  journal = {Annales Scientifiques de l'{\'E}cole Normale Sup{\'e}rieure},
  series = {4},
  volume = {49},
  number = {1},
  year = {2016},
  pages = {169--212},
  doi = {10.24033/asens.2279},
  eprint = {1311.3098},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/html/1311.3098v2},
  note = {Theorem numbering checked in arXiv version 2, 16 October 2014}
}

@article{hnt2020,
  author = {Hashizume, Kenta and Nakamura, Yusuke and Tanaka, Hiromu},
  title = {Minimal Model Program for Log Canonical Threefolds in Positive Characteristic},
  journal = {Mathematical Research Letters},
  volume = {27},
  number = {4},
  year = {2020},
  pages = {1003--1054},
  doi = {10.4310/MRL.2020.v27.n4.a3},
  eprint = {1711.10706},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1711.10706}
}

@article{hw2022,
  author = {Hacon, Christopher and Witaszek, Jakub},
  title = {The Minimal Model Program for Threefolds in Characteristic {$5$}},
  journal = {Duke Mathematical Journal},
  volume = {171},
  number = {11},
  year = {2022},
  pages = {2193--2231},
  doi = {10.1215/00127094-2022-0024},
  eprint = {1911.12895},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1911.12895}
}

@article{langer2004,
  author = {Langer, Adrian},
  title = {Semistable Sheaves in Positive Characteristic},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {159},
  number = {1},
  year = {2004},
  pages = {251--276},
  doi = {10.4007/annals.2004.159.251},
  url = {https://annals.math.princeton.edu/wp-content/uploads/annals-v159-n1-p04.pdf}
}

@article{langeradd2004,
  author = {Langer, Adrian},
  title = {Addendum to {``Semistable Sheaves in Positive Characteristic''}},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {160},
  number = {3},
  year = {2004},
  pages = {1211--1213},
  doi = {10.4007/annals.2004.160.1211},
  url = {https://annals.math.princeton.edu/wp-content/uploads/annals-v160-n3-p10.pdf}
}

@article{langer2015,
  author = {Langer, Adrian},
  title = {Generic Positivity and Foliations in Positive Characteristic},
  journal = {Advances in Mathematics},
  volume = {277},
  year = {2015},
  pages = {1--23},
  doi = {10.1016/j.aim.2015.02.015},
  url = {https://www.sciencedirect.com/science/article/pii/S0001870815000870}
}

@article{xuzhang2019,
  author = {Xu, Chenyang and Zhang, Lei},
  title = {Nonvanishing for Threefolds in Characteristic {$p>5$}},
  journal = {Duke Mathematical Journal},
  volume = {168},
  number = {7},
  year = {2019},
  pages = {1269--1301},
  doi = {10.1215/00127094-2018-0066},
  eprint = {1801.03192},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/html/1801.03192v3}
}

@article{jlr2026,
  author = {Jovinelly, Eric and Lehmann, Brian and Riedl, Eric},
  title = {Optimal Bounds in {Bend-and-Break}},
  journal = {Forum of Mathematics, Pi},
  volume = {14},
  year = {2026},
  pages = {1--4},
  doi = {10.1017/fmp.2026.10033},
  url = {https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/optimal-bounds-in-bendandbreak/9F6B18C8191A1E3EC9E6C05F8DF2EDC7},
  note = {Article e16; published online 6 May 2026}
}

@article{katz1970,
  author = {Katz, Nicholas M.},
  title = {Nilpotent Connections and the Monodromy Theorem: Applications of a Result of {Turrittin}},
  journal = {Publications Math\'{e}matiques de l'IH\'{E}S},
  volume = {39},
  year = {1970},
  pages = {175--232},
  doi = {10.1007/BF02684688},
  url = {https://www.numdam.org/item/PMIHES_1970__39__175_0/}
}

@book{hartshorne1977,
  author = {Hartshorne, Robin},
  title = {Algebraic Geometry},
  series = {Graduate Texts in Mathematics},
  volume = {52},
  publisher = {Springer-Verlag},
  address = {New York},
  year = {1977},
  doi = {10.1007/978-1-4757-3849-0},
  url = {https://link.springer.com/book/10.1007/978-1-4757-3849-0}
}

@book{hartshorne1966,
  author = {Hartshorne, Robin},
  title = {Residues and Duality},
  series = {Lecture Notes in Mathematics},
  volume = {20},
  publisher = {Springer-Verlag},
  address = {Berlin--Heidelberg},
  year = {1966},
  doi = {10.1007/BFb0080482},
  url = {https://link.springer.com/book/10.1007/BFb0080482},
  note = {Lecture notes of a seminar on the work of A. Grothendieck, Harvard 1963/64}
}

@book{hartshorne1967,
  author = {Hartshorne, Robin},
  title = {Local Cohomology},
  series = {Lecture Notes in Mathematics},
  volume = {41},
  publisher = {Springer-Verlag},
  address = {Berlin--Heidelberg},
  year = {1967},
  doi = {10.1007/BFb0073971},
  url = {https://link.springer.com/book/10.1007/BFb0073971},
  note = {A seminar given by A. Grothendieck, Harvard University, Fall 1961; notes by R. Hartshorne}
}

@book{fulton1998,
  author = {Fulton, William},
  title = {Intersection Theory},
  edition = {2},
  series = {Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge},
  volume = {2},
  publisher = {Springer-Verlag},
  address = {Berlin},
  year = {1998},
  doi = {10.1007/978-1-4612-1700-8},
  url = {https://link.springer.com/book/10.1007/978-1-4612-1700-8}
}

@book{kollar1996,
  author = {Koll\'{a}r, J\'{a}nos},
  title = {Rational Curves on Algebraic Varieties},
  series = {Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge},
  volume = {32},
  publisher = {Springer-Verlag},
  address = {Berlin--Heidelberg},
  year = {1996},
  doi = {10.1007/978-3-662-03276-3},
  url = {https://link.springer.com/book/10.1007/978-3-662-03276-3}
}

@book{kollarMori1998,
  author = {Koll\'{a}r, J\'{a}nos and Mori, Shigefumi},
  title = {Birational Geometry of Algebraic Varieties},
  series = {Cambridge Tracts in Mathematics},
  volume = {134},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {1998},
  doi = {10.1017/CBO9780511662560},
  url = {https://www.cambridge.org/core/books/birational-geometry-of-algebraic-varieties/FB73FD7FDC65F023521ED6B1BB7F3EC7},
  note = {With the collaboration of C. H. Clemens and A. Corti}
}

@article{cossartpiltant2008,
  author = {Cossart, Vincent and Piltant, Olivier},
  title = {Resolution of Singularities of Threefolds in Positive Characteristic. {I}. Reduction to Local Uniformization on {Artin--Schreier} and Purely Inseparable Coverings},
  journal = {Journal of Algebra},
  volume = {320},
  number = {3},
  year = {2008},
  pages = {1051--1082},
  doi = {10.1016/j.jalgebra.2008.03.032},
  url = {https://www.sciencedirect.com/science/article/pii/S0021869308001853}
}

@article{cp2009,
  author = {Cossart, Vincent and Piltant, Olivier},
  title = {Resolution of Singularities of Threefolds in Positive Characteristic {II}},
  journal = {Journal of Algebra},
  volume = {321},
  number = {7},
  year = {2009},
  pages = {1836--1976},
  doi = {10.1016/j.jalgebra.2008.11.030},
  url = {https://www.sciencedirect.com/science/article/pii/S0021869308005942}
}

@article{cp2019,
  author = {Cossart, Vincent and Piltant, Olivier},
  title = {Resolution of Singularities of Arithmetical Threefolds},
  journal = {Journal of Algebra},
  volume = {529},
  year = {2019},
  pages = {268--535},
  doi = {10.1016/j.jalgebra.2019.02.017},
  url = {https://www.sciencedirect.com/science/article/pii/S0021869319301061}
}

@misc{cjs2009,
  author = {Cossart, Vincent and Jannsen, Uwe and Saito, Shuji},
  title = {Canonical Embedded and Non-Embedded Resolution of Singularities for Excellent Two-Dimensional Schemes},
  year = {2009},
  eprint = {0905.2191},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/0905.2191},
  note = {First posted 13 May 2009; version 2, 18 February 2013}
}

@book{cjs2020,
  author = {Cossart, Vincent and Jannsen, Uwe and Saito, Shuji},
  title = {Desingularization: Invariants and Strategy: Application to Dimension {$2$}},
  series = {Lecture Notes in Mathematics},
  volume = {2270},
  publisher = {Springer},
  address = {Cham},
  year = {2020},
  doi = {10.1007/978-3-030-52640-5},
  url = {https://link.springer.com/book/10.1007/978-3-030-52640-5},
  note = {With contributions by Bernd Schober}
}

@incollection{bauer2004,
  author = {Bauer, Thomas and Campana, Fr\'{e}d\'{e}ric and Eckl, Thomas and Kebekus, Stefan and Peternell, Thomas and Rams, S{\l}awomir and Szemberg, Tomasz and Wotzlaw, Lorenz},
  title = {A Reduction Map for Nef Line Bundles},
  booktitle = {Complex Geometry: Collection of Papers Dedicated to Hans Grauert},
  editor = {Bauer, Ingrid and Catanese, Fabrizio and Peternell, Thomas and Kawamata, Yujiro and Siu, Yum-Tong},
  publisher = {Springer},
  address = {Berlin--Heidelberg},
  year = {2002},
  pages = {27--36},
  doi = {10.1007/978-3-642-56202-0_2},
  url = {https://link.springer.com/chapter/10.1007/978-3-642-56202-0_2}
}

@article{egaIII,
  author = {Grothendieck, Alexander},
  title = {\'{E}l\'{e}ments de g\'{e}om\'{e}trie alg\'{e}brique. {III}. \'{E}tude cohomologique des faisceaux coh\'{e}rents. {Premi\`ere partie}},
  journal = {Publications Math\'{e}matiques de l'IH\'{E}S},
  volume = {11},
  year = {1961},
  pages = {5--167},
  url = {https://www.numdam.org/item/PMIHES_1961__11__5_0/},
  note = {Written with the collaboration of Jean Dieudonn\'{e}}
}

@article{egaIII2,
  author = {Grothendieck, Alexander},
  title = {\'{E}l\'{e}ments de g\'{e}om\'{e}trie alg\'{e}brique. {III}. \'{E}tude cohomologique des faisceaux coh\'{e}rents. {Seconde partie}},
  journal = {Publications Math\'{e}matiques de l'IH\'{E}S},
  volume = {17},
  year = {1963},
  pages = {5--91},
  url = {https://www.numdam.org/item/PMIHES_1963__17__5_0/},
  note = {Written with the collaboration of Jean Dieudonn\'{e}}
}

@book{jouanolou1983,
  author = {Jouanolou, Jean-Pierre},
  title = {Th\'{e}or\`emes de {Bertini} et applications},
  series = {Progress in Mathematics},
  volume = {42},
  publisher = {Birkh\"auser},
  year = {1983},
  isbn = {3-7643-3164-X}
}

@article{kleiman1966,
  author = {Kleiman, Steven L.},
  title = {Toward a Numerical Theory of Ampleness},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {84},
  number = {3},
  year = {1966},
  pages = {293--344},
  doi = {10.2307/1970447},
  url = {https://annals.math.princeton.edu/1966/84-3/p01}
}

@misc{liuxu2025,
  author = {Liu, Jihao and Xu, Zheng},
  title = {Non-vanishing Implies Numerical Dimension One Abundance},
  year = {2025},
  eprint = {2505.05250},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/html/2505.05250v2},
  note = {Version 2, 30 July 2025}
}

@article{witaszek2021,
  author = {Witaszek, Jakub},
  title = {On the Canonical Bundle Formula and Log Abundance in Positive Characteristic},
  journal = {Mathematische Annalen},
  volume = {381},
  number = {3--4},
  year = {2021},
  pages = {1309--1344},
  doi = {10.1007/s00208-021-02231-5},
  eprint = {1711.04380},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://link.springer.com/article/10.1007/s00208-021-02231-5}
}

@article{zhang2020,
  author = {Zhang, Lei},
  title = {Abundance for {$3$}-folds with Non-trivial {Albanese} Maps in Positive Characteristic},
  journal = {Journal of the European Mathematical Society},
  volume = {22},
  number = {9},
  year = {2020},
  pages = {2777--2820},
  doi = {10.4171/JEMS/977},
  eprint = {1705.00847},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://ems.press/journals/jems/articles/16960}
}

@misc{stacks,
  author = {{The Stacks Project Authors}},
  title = {{The Stacks Project}},
  year = {2026},
  howpublished = {Online reference},
  url = {https://stacks.math.columbia.edu},
  note = {Accessed 10 September 2026}
}

@article{miyaoka1988,
  author = {Miyaoka, Yoichi},
  title = {Abundance Conjecture for {$3$}-folds: Case {$\nu=1$}},
  journal = {Compositio Mathematica},
  volume = {68},
  number = {2},
  pages = {203--220},
  year = {1988},
  url = {https://numdam.org/item/CM_1988__68_2_203_0/}
}

@article{kawamata1992,
  author = {Kawamata, Yujiro},
  title = {Abundance Theorem for Minimal Threefolds},
  journal = {Inventiones Mathematicae},
  volume = {108},
  pages = {229--246},
  year = {1992},
  doi = {10.1007/BF02100604},
  url = {https://doi.org/10.1007/BF02100604}
}

@article{cartier1957,
  author = {Cartier, Pierre},
  title = {Une nouvelle op{\'e}ration sur les formes diff{\'e}rentielles},
  journal = {Comptes rendus de l'Acad{\'e}mie des sciences de Paris},
  volume = {244},
  year = {1957},
  pages = {426--428},
  url = {https://www.ihes.fr/wp-content/uploads/2024/09/CartierCRAS57.pdf}
}

@article{esnaultmehta2010,
  author = {Esnault, H{\'e}l{\`e}ne and Mehta, Vikram},
  title = {Simply connected projective manifolds in characteristic {$p>0$}
           have no nontrivial stratified bundles},
  journal = {Inventiones Mathematicae},
  volume = {181},
  year = {2010},
  pages = {449--465},
  doi = {10.1007/s00222-010-0250-2},
  eprint = {0907.3375},
  archivePrefix = {arXiv},
  primaryClass = {math.AG}
}

@article{tanaka2016,
  author = {Tanaka, Hiromu},
  title = {Abundance Theorem for Semi Log Canonical Surfaces in Positive Characteristic},
  journal = {Osaka Journal of Mathematics},
  volume = {53},
  number = {2},
  year = {2016},
  pages = {535--566},
  doi = {10.18910/58879},
  eprint = {1301.6889},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://ir.library.osaka-u.ac.jp/repo/ouka/all/58879/}
}

@misc{cossart2008notes,
  author = {Cossart, Vincent},
  title = {Resolution of Singularities of Threefolds in Positive Characteristic},
  year = {2008},
  howpublished = {Lecture notes, RIMS workshop ``On the Resolution of Singularities'', Kyoto, 1--5 December 2008},
  url = {https://www.kurims.kyoto-u.ac.jp/~kenkyubu/proj08-mori/confkyoto.pdf}
}

@misc{totaro2007,
  author = {Totaro, Burt},
  title = {Moving Codimension-One Subvarieties over Finite Fields},
  year = {2007},
  eprint = {0712.2049},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/0712.2049v1},
  note = {\href{https://arxiv.org/abs/0712.2049v1}{arXiv:0712.2049v1}, 12 December 2007}
}
