@incollection{Hochster2017,
  author = {Hochster, Melvin},
  title = {Homological conjectures and lim {Cohen--Macaulay} sequences},
  booktitle = {Homological and Computational Methods in Commutative Algebra},
  series = {Springer INdAM Series},
  volume = {20},
  pages = {173--197},
  publisher = {Springer},
  year = {2017},
  doi = {10.1007/978-3-319-61943-9_11},
  url = {https://sites.lsa.umich.edu/hochster/wp-content/uploads/sites/1337/2024/08/DSlim2.pdf}
}

@article{BhattHochsterMa,
  author = {Bhatt, Bhargav and Hochster, Mel and Ma, Linquan},
  title = {Lim {Cohen--Macaulay} sequences of modules},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume = {835},
  pages = {111--169},
  year = {2026},
  eprint = {2410.18372v2},
  archivePrefix = {arXiv},
  primaryClass = {math.AC},
  note = {Numbered references follow \href{https://arxiv.org/abs/2410.18372v2}{arXiv:2410.18372v2}, August 25, 2026},
  url = {https://arxiv.org/abs/2410.18372v2}
}

@article{Bhatt2014,
  author = {Bhatt, Bhargav},
  title = {On the non-existence of small {Cohen--Macaulay} algebras},
  journal = {Journal of Algebra},
  volume = {411},
  pages = {1--11},
  year = {2014},
  doi = {10.1016/j.jalgebra.2014.03.038}
}

@article{HochsterHuneke1992,
  author = {Hochster, Melvin and Huneke, Craig},
  title = {Infinite integral extensions and big {Cohen--Macaulay} algebras},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {135},
  number = {1},
  pages = {53--89},
  year = {1992},
  doi = {10.2307/2946563}
}

@article{Andre2018,
  author = {Andr\'e, Yves},
  title = {La conjecture du facteur direct},
  journal = {Publications Math\'ematiques de l'IH\'ES},
  volume = {127},
  pages = {71--93},
  year = {2018},
  doi = {10.1007/s10240-017-0097-9}
}

@article{HochsterYao2023,
  author = {Hochster, Melvin and Yao, Yongwei},
  title = {{Frobenius} splitting, strong {$F$}-regularity, and small
           {Cohen--Macaulay} modules},
  journal = {Transactions of the American Mathematical Society},
  volume = {376},
  number = {9},
  pages = {6729--6765},
  year = {2023},
  doi = {10.1090/tran/8964}
}

@book{HuybrechtsLehn,
  author = {Huybrechts, Daniel and Lehn, Manfred},
  title = {The Geometry of Moduli Spaces of Sheaves},
  series = {Aspects of Mathematics},
  volume = {E31},
  publisher = {Friedr. Vieweg \& Sohn},
  address = {Braunschweig},
  year = {1997}
}

@book{Hartshorne,
  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}
}

@incollection{Hirzebruch1983,
  author = {Hirzebruch, Friedrich},
  title = {Arrangements of lines and algebraic surfaces},
  booktitle = {Arithmetic and Geometry, Vol.~II},
  editor = {Artin, Michael and Tate, John},
  series = {Progress in Mathematics},
  volume = {36},
  pages = {113--140},
  publisher = {Birkh\"auser},
  address = {Boston},
  year = {1983},
  doi = {10.1007/978-1-4757-9286-7_7},
  url = {https://hirzebruch.mpim-bonn.mpg.de/id/eprint/244/}
}

@misc{Anghel2026,
  author = {Anghel, Cristian},
  title = {Smooth Counterexamples to the {Eisenbud--Schreyer--Weyman} {Ulrich} Existence Problem},
  year = {2026},
  eprint = {2609.02718v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  note = {\href{https://arxiv.org/abs/2609.02718v1}{arXiv:2609.02718v1}, September 2, 2026},
  url = {https://arxiv.org/abs/2609.02718v1}
}

@misc{Stacks,
  author = {{The Stacks Project Authors}},
  title = {The {Stacks} Project},
  year = {2026},
  url = {https://stacks.math.columbia.edu}
}

@book{Hochster1975,
  author = {Hochster, Melvin},
  title = {Topics in the Homological Theory of Modules over Commutative Rings},
  series = {CBMS Regional Conference Series in Mathematics},
  volume = {24},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {1975},
  doi = {10.1090/cbms/024}
}
@article{EisenbudSchreyer2003,
  author = {Eisenbud, David and Schreyer, Frank-Olaf},
  title = {Resultants and {Chow} forms via exterior syzygies},
  journal = {Journal of the American Mathematical Society},
  volume = {16},
  number = {3},
  pages = {537--579},
  year = {2003},
  note = {With an appendix by Jerzy Weyman},
  url = {https://arxiv.org/abs/math/0111040}
}

@incollection{Hochster1973,
  author = {Hochster, Melvin},
  title = {{Cohen--Macaulay} modules},
  booktitle = {Conference on Commutative Algebra (Lawrence, 1972)},
  editor = {Brewer, James W. and Rutter, Edgar A.},
  series = {Lecture Notes in Mathematics},
  volume = {311},
  pages = {120--152},
  publisher = {Springer},
  year = {1973},
  doi = {10.1007/BFb0068925}
}

@misc{Chen2026,
  author = {Chen, Liang},
  title = {A local cohomology obstruction to small {Cohen--Macaulay} modules},
  year = {2026},
  eprint = {2609.24142v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  note = {\href{https://arxiv.org/abs/2609.24142v1}{arXiv:2609.24142v1}, September 21, 2026},
  url = {https://arxiv.org/abs/2609.24142v1}
}

@misc{Anghel2026Graded,
  author = {Anghel, Cristian},
  title = {Polarized varieties without arithmetically {Cohen--Macaulay} bundles and section rings without graded maximal {Cohen--Macaulay} modules in characteristic zero},
  year = {2026},
  eprint = {2609.15589v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  note = {\href{https://arxiv.org/abs/2609.15589v1}{arXiv:2609.15589v1}, September 14, 2026},
  url = {https://arxiv.org/abs/2609.15589v1}
}

@article{ChenSun2020,
  author = {Chen, Xuemiao and Sun, Song},
  title = {Algebraic tangent cones of reflexive sheaves},
  journal = {International Mathematics Research Notices},
  volume = {2020},
  number = {24},
  pages = {10042--10063},
  year = {2020},
  doi = {10.1093/imrn/rny276}
}

@misc{Beauville2017,
  author = {Beauville, Arnaud},
  title = {Ulrich bundles: to be or not to be},
  year = {2017},
  month = oct,
  howpublished = {Lecture slides, Beijing},
  note = {\href{https://math.univ-cotedazur.fr/u/beauvill/conf/Ulrich.pdf}{Author's slides}},
  url = {https://math.univ-cotedazur.fr/u/beauvill/conf/Ulrich.pdf}
}

@article{Behrend2009,
  author = {Behrend, Kai},
  title = {{Donaldson--Thomas} type invariants via microlocal geometry},
  journal = {Annals of Mathematics},
  volume = {170},
  number = {3},
  pages = {1307--1338},
  year = {2009},
  doi = {10.4007/annals.2009.170.1307}
}