leuschke.org

Papers

Articles and preprints

Reverse chronological. Each paper links its DOI, its arXiv version, and a PDF, where the three exist — the earliest papers here predate my getting into the habit of posting preprints.

The two books have their own pages: Cohen–Macaulay Representations, with Roger Wiegand, and Twenty-Four Hours of Local Cohomology, by seven authors. There is also this article for the MSRI newsletter about noncommutative resolutions, which I have never known where to put.

  1. Characteristic-free Knörrer periodicity. Preprint, 2026. arXiv · pdf (version of 2026-09-29)
  2. Cover of the Bulletin of the London Mathematical Society
    Branched covers and matrix factorizations. With Tim Tribone. Bull. London Math. Soc. 55 (2023), no. 6, 2907–2927. doi · arXiv · pdf
  3. Cover of Journal of Algebra
    Some extensions of theorems of Knörrer and Herzog–Popescu. With Alex Dugas. J. Algebra 571 (2021), 94–120. doi · arXiv · pdf
  4. Cover of International Mathematics Research Notices
    Non-commutative desingularization of determinantal varieties, II: Arbitrary minors. With Ragnar-Olaf Buchweitz and Michel Van den Bergh. Int. Math. Res. Not. 2016, no. 9, 2748–2812. doi · arXiv · pdf (version of 2013-10-01)
  5. Cover of Compositio Mathematica
    On the derived category of Grassmannians in arbitrary characteristic. With Ragnar-Olaf Buchweitz and Michel Van den Bergh. Compos. Math. 151 (2015), no. 7, 1242–1264. doi · arXiv · pdf
  6. Cover of Commutative Algebra: Expository Papers Dedicated to David Eisenbud
    Brauer–Thrall theory for maximal Cohen-Macaulay modules. With Roger Wiegand. In Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of his 65th Birthday, 577–592, Springer, 2013. doi · arXiv · pdf
  7. Cover of Progress in Commutative Algebra 1
    Non-commutative crepant resolutions: scenes from categorical geometry. In Progress in Commutative Algebra 1, 293–361, de Gruyter, 2012. doi · arXiv · pdf (version of 2011-08-22)
  8. Cover of Collectanea Mathematica
    Presentations of rings with non-trivial semidualizing modules. With David Jorgensen and Keri Sather-Wagstaff. Collect. Math. 63 (2012), no. 2, 165–180. doi · arXiv · pdf (final version, 8 Oct 2010)
  9. Cover of Journal of Pure and Applied Algebra
    Wild hypersurfaces. With Andrew Crabbe. J. Pure Appl. Algebra 215 (2011), 2884–2891. doi · arXiv · pdf (version of 2011-03-08)
  10. Cover of Inventiones Mathematicae
    Non-commutative desingularization of determinantal varieties, I: Maximal minors. With Ragnar-Olaf Buchweitz and Michel Van den Bergh. Invent. Math. 182 (2010), no. 1, 47–115. doi · arXiv · pdf
  11. Cover of American Journal of Mathematics
    Factoring the adjoint and maximal Cohen-Macaulay modules over the generic determinant. With Ragnar-Olaf Buchweitz. Amer. J. Math. 129 (2007), no. 4, 943–981. doi · arXiv · pdf
  12. Cover of Mathematische Zeitschrift
    On the growth of the Betti sequence of the canonical module. With David Jorgensen. Math. Z. 256 (2007), no. 3, 647–659. doi · arXiv · pdf · erratum Three results in Section 2 are incorrect as stated. The erratum corrects Lemma 2.1 by moving the range of indices for which Ext vanishes, and adjusts Theorems 2.2 and 2.4 to match.
  13. Cover of Canadian Journal of Mathematics
    Endomorphism rings of finite global dimension. Canad. J. Math. 59 (2007), no. 2, 332–342. doi · arXiv · pdf · erratum · addendum The erratum fixes the proof of Theorem 6 and admits falsehoods in a couple of places; the addendum computes the global dimension of the endomorphism ring in Example 12. (It is 4.)
  14. Cover of Trends in Commutative Algebra
    Appendix: some examples in tight closure. Appendix to “Tight closure theory and characteristic p methods,” by M. Hochster, in Trends in Commutative Algebra, MSRI Publications 51, 181–210, Cambridge University Press, 2004. pdf
  15. Cover of Algebras and Representation Theory
    Local rings of bounded Cohen-Macaulay type. With Roger Wiegand. Algebr. Represent. Theory 8 (2005), no. 2, 225–238. doi · arXiv · pdf
  16. Cover of Journal of Pure and Applied Algebra
    Hypersurfaces of bounded Cohen-Macaulay type. With Roger Wiegand. J. Pure Appl. Algebra 201 (2005), no. 1–3, 204–217. doi · arXiv · pdf · addendum “Large indecomposable MCM modules,” with Roger Wiegand: a direct construction showing that S[Z]/(Z2) has unbounded Cohen–Macaulay type whenever S is Cohen–Macaulay local of dimension at least two.
  17. Cover of Journal of Algebra
    On a conjecture of Auslander and Reiten. With Craig Huneke. J. Algebra 275 (2004), no. 2, 781–790. doi · arXiv · pdf
  18. Cover of Mathematical Research Letters
    The F-signature and strong F-regularity. With Ian Aberbach. Math. Res. Lett. 10 (2003), no. 1, 51–56. doi · arXiv · pdf
  19. Cover of Proceedings of the American Mathematical Society
    Local rings of countable Cohen-Macaulay type. With Craig Huneke. Proc. Amer. Math. Soc. 131 (2003), 3003–3007. doi · arXiv · pdf
  20. Cover of Mathematische Annalen
    Two theorems about maximal Cohen-Macaulay modules. With Craig Huneke. Math. Ann. 324 (2002), no. 2, 391–404. doi · arXiv · pdf
  21. Cover of Communications in Algebra
    Gorenstein modules, finite index, and finite Cohen-Macaulay type. Comm. Algebra 30 (2002), no. 4, 2023–2035. doi · pdf
  22. Cover of Journal of Pure and Applied Algebra
    Mixed-characteristic hypersurfaces of finite Cohen-Macaulay type. J. Pure Appl. Algebra 167 (2002), no. 2–3, 225–257. doi · pdf
  23. Cover of Journal of Algebra
    Ascent of finite Cohen-Macaulay type. With Roger Wiegand. J. Algebra 228 (2000), no. 2, 674–681. doi · pdf

Also: my dissertation, Finite Cohen-Macaulay Type (Nebraska, 2000). This research has been supported by NSF grants DMS-0902119 and DMS-0556181, by grants from the NSA, and by the Clay Mathematics Institute.