@article{Bass1960,
  author  = {Bass, Hyman},
  title   = {Finitistic dimension and a homological generalization of semi-primary rings},
  journal = {Transactions of the American Mathematical Society},
  volume  = {95},
  number  = {3},
  year    = {1960},
  pages   = {466--488},
  doi     = {10.1090/S0002-9947-1960-0157984-8},
  url     = {https://doi.org/10.1090/S0002-9947-1960-0157984-8},
  note    = {\href{https://doi.org/10.1090/S0002-9947-1960-0157984-8}{Publisher DOI}}
}

@article{Rego2022,
  author  = {Santos Rego, Yuri},
  title   = {On the finiteness length of some soluble linear groups},
  journal = {Canadian Journal of Mathematics},
  volume  = {74},
  number  = {5},
  year    = {2022},
  pages   = {1209--1243},
  doi     = {10.4153/S0008414X21000213},
  eprint  = {1901.06704},
  archivePrefix = {arXiv},
  primaryClass = {math.GR},
  url     = {https://arxiv.org/abs/1901.06704v3},
  note    = {\href{https://doi.org/10.4153/S0008414X21000213}{Publisher DOI};
             \href{https://arxiv.org/abs/1901.06704v3}{arXiv:1901.06704v3}}
}

@article{NRS2004,
  author  = {Neeman, Amnon and Ranicki, Andrew and Schofield, Aidan},
  title   = {Representations of algebras as universal localizations},
  journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
  volume  = {136},
  number  = {1},
  year    = {2004},
  pages   = {105--117},
  doi     = {10.1017/S030500410300700X},
  eprint  = {math/0205034},
  archivePrefix = {arXiv},
  url     = {https://arxiv.org/abs/math/0205034v2},
  note    = {\href{https://doi.org/10.1017/S030500410300700X}{Publisher DOI};
             \href{https://arxiv.org/abs/math/0205034v2}{arXiv:math/0205034v2}}
}

@article{BalmerSchlichting2001,
  author  = {Balmer, Paul and Schlichting, Marco},
  title   = {Idempotent completion of triangulated categories},
  journal = {Journal of Algebra},
  volume  = {236},
  number  = {2},
  year    = {2001},
  pages   = {819--834},
  doi     = {10.1006/jabr.2000.8529},
  url     = {https://doi.org/10.1006/jabr.2000.8529},
  note    = {\href{https://doi.org/10.1006/jabr.2000.8529}{Publisher DOI};
             \href{https://webhomes.maths.ed.ac.uk/~v1ranick/papers/balmschl.pdf}{full text}}
}

@article{Keller2000,
  author  = {Keller, Bernhard},
  title   = {Bimodule complexes via strong homotopy actions},
  journal = {Algebras and Representation Theory},
  volume  = {3},
  number  = {4},
  year    = {2000},
  pages   = {357--376},
  doi     = {10.1023/A:1009954126727},
  eprint  = {math/9910178},
  archivePrefix = {arXiv},
  url     = {https://arxiv.org/abs/math/9910178v1},
  note    = {\href{https://doi.org/10.1023/A:1009954126727}{Publisher DOI};
             \href{https://arxiv.org/abs/math/9910178v1}{arXiv:math/9910178v1}}
}

@article{MinamotoYamaura,
  author  = {Minamoto, Hiroyuki and Yamaura, Kota},
  title   = {Homological dimension formulas for trivial extension algebras},
  journal = {Journal of Pure and Applied Algebra},
  volume  = {224},
  number  = {8},
  year    = {2020},
  pages   = {106344},
  doi     = {10.1016/j.jpaa.2020.106344},
  eprint  = {1710.01469},
  archivePrefix = {arXiv},
  primaryClass = {math.RA},
  url     = {https://arxiv.org/abs/1710.01469v1},
  note    = {30 pp.
             \href{https://doi.org/10.1016/j.jpaa.2020.106344}{Publisher DOI};
             \href{https://arxiv.org/abs/1710.01469v1}{arXiv:1710.01469v1}.
             All result numbers in citations to this paper refer to this arXiv version}
}

@misc{StacksProject,
  author = {{The Stacks Project Authors}},
  title  = {The {Stacks} project},
  year   = {2026},
  howpublished = {\url{https://stacks.math.columbia.edu}},
  url    = {https://stacks.math.columbia.edu},
  note   = {Tags \href{https://stacks.math.columbia.edu/tag/04VI}{04VI},
            \href{https://stacks.math.columbia.edu/tag/04VJ}{04VJ},
            \href{https://stacks.math.columbia.edu/tag/05RG}{05RG}, and
            \href{https://stacks.math.columbia.edu/tag/05RJ}{05RJ};
            accessed 23 September 2026}
}

@article{HuisgenZimmermann1992,
  author = {Zimmermann Huisgen, Birge},
  title = {Homological domino effects and the first {Finitistic Dimension Conjecture}},
  journal = {Inventiones Mathematicae},
  volume = {108},
  year = {1992},
  pages = {369--383},
  doi = {10.1007/BF02100610},
  note = {\href{https://doi.org/10.1007/BF02100610}{Publisher DOI}}
}

@article{GreenKirkmanKuzmanovich1991,
  author = {Green, Edward L. and Kirkman, Ellen E. and Kuzmanovich, James},
  title = {Finitistic dimensions of finite dimensional monomial algebras},
  journal = {Journal of Algebra},
  volume = {136},
  number = {1},
  year = {1991},
  pages = {37--50},
  doi = {10.1016/0021-8693(91)90062-D},
  note = {\href{https://doi.org/10.1016/0021-8693(91)90062-D}{Publisher DOI}}
}

@article{GreenHuisgenZimmermann1991,
  author = {Green, Edward L. and Zimmermann Huisgen, Birge},
  title = {Finitistic dimension of {Artinian} rings with vanishing radical cube},
  journal = {Mathematische Zeitschrift},
  volume = {206},
  number = {4},
  year = {1991},
  pages = {505--526}
}

@incollection{IgusaTodorov2005,
  author = {Igusa, Kiyoshi and Todorov, Gordana},
  title = {On the finitistic global dimension conjecture for {Artin} algebras},
  booktitle = {Representations of Algebras and Related Topics},
  series = {Fields Institute Communications},
  volume = {45},
  publisher = {American Mathematical Society},
  address = {Providence, RI},
  year = {2005},
  pages = {201--204}
}

@article{Rickard2019,
  author = {Rickard, Jeremy},
  title = {Unbounded derived categories and the finitistic dimension conjecture},
  journal = {Advances in Mathematics},
  volume = {354},
  year = {2019},
  pages = {106735},
  doi = {10.1016/j.aim.2019.106735},
  eprint = {1804.09801},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1804.09801v1},
  note = {\href{https://doi.org/10.1016/j.aim.2019.106735}{Publisher DOI};
    \href{https://arxiv.org/abs/1804.09801v1}{arXiv:1804.09801v1}}
}

@incollection{HuisgenZimmermann1995,
  author = {Zimmermann Huisgen, Birge},
  title = {The finitistic dimension conjectures---a tale of 3.5 decades},
  booktitle = {Abelian Groups and Modules},
  editor = {Facchini, Alberto and Menini, Claudia},
  series = {Mathematics and Its Applications},
  volume = {343},
  publisher = {Kluwer Academic Publishers},
  address = {Dordrecht},
  year = {1995},
  pages = {501--517},
  doi = {10.1007/978-94-011-0443-2_41},
  eprint = {1407.2383},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1407.2383v1},
  note = {\href{https://doi.org/10.1007/978-94-011-0443-2_41}{Publisher DOI};
    \href{https://arxiv.org/abs/1407.2383v1}{arXiv:1407.2383v1}}
}

@article{Cummings2024,
  author = {Cummings, Charley},
  title = {Left--right symmetry of finite finitistic dimension},
  journal = {Bulletin of the London Mathematical Society},
  volume = {56},
  number = {2},
  year = {2024},
  pages = {624--633},
  doi = {10.1112/blms.12954},
  eprint = {2211.04394},
  archivePrefix = {arXiv},
  note = {\href{https://doi.org/10.1112/blms.12954}{Publisher DOI}}
}

@misc{OpenAITachikawa2026,
  author = {{OpenAI}},
  title = {{A counterexample to Tachikawa's second conjecture}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Tachikawas-second-conjecture-September-23-2026/paper.pdf}{OAI:A-counterexample-to-Tachikawas-second-conjecture-September-23-2026}},
  year = {2026}
}