Research Publications

A list of all of my available papers and preprints can be found on the arXiv: http://arxiv.org/a/thompson_p_1.

Papers

  1. The singularity category of an exact category with applications to the flat–cotorsion theory. Joint with L. W. Christensen, N. Ding, S. Estrada, J. Hu, and H. Li. The Quarterly Journal of Mathematics, to appear.
    2. [Links: journal, arxiv]
  2. Five theorems on Gorenstein global dimensions. Joint with L. W. Christensen and S. Estrada. Contemporary Mathematics, to appear.
    3. [Links: journal, arxiv]
  3. Asymptotic behavior of Ext for pairs of modules of large complexity over graded complete intersections. Joint with D. Jorgensen and L. Sega. Mathematische Zeitschrift, (2022).
    4. [Links: journal, arxiv]
  4. Gorenstein weak global dimension is symmetric. Joint with L. W. Christensen and S. Estrada. Mathematische Nachrichten, 294 (2021).
    5. [Links: journal, arxiv]
  5. Matrix factorizations for self-orthogonal categories of modules. Joint with P. A. Bergh. Journal of Algebra and Its Applications, 20 (2021), no. 3, 22 pp.
    6. [Links: journal, arxiv]
  6. Reducibility of parameter ideals in low powers of the maximal ideal. Joint with K. Shultis. Contemporary Mathematics, 773 (2021), 218-193.
    7. [Links: journal, arxiv]
  7. The stable category of Gorenstein flat sheaves on a noetherian scheme. Joint with L. W. Christensen and S. Estrada. Proceedings of the American Mathematical Society, to appear.
    8. [Links: journal, arxiv]
  8. A refinement of Gorenstein flat dimension via the flat--cotorsion theory. Joint with L. W. Christensen, S. Estrada, L. Liang, D. Wu, and G. Yang. Journal of Algebra 567 (2021), 346-370.
    9. [Links: journal, arxiv]
  9. Minimal semi-flat-cotorsion replacements and cosupport. Joint with T. Nakamura. Journal of Algebra 562 (2020), 587-620.
    10. [Links: journal (open access), arxiv]
  10. Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory. Joint with L. W. Christensen and S. Estrada. To appear in Contemporary Mathematics.
    11. [Links: journal, arxiv]
  11. Detecting Koszulness and related homological properties from the algebra structure of Koszul homology. Joint with A. Croll, R. Dellaca, A. Gupta, D. Rangel Tracy, J. Hoffmeier, L. Sega, G. Sosa. Nagoya Mathematical Journal 238 (2020), 47-85.
    12. [Links: journal, arxiv]
  12. Pure-minimal chain complexes. Joint with L. W. Christensen. Rendiconti del Seminario Matematico della Università di Padova 142 (2019) 41-67.
    13. [Links: journal, arxiv]
  13. Minimal complexes of cotorsion flat modules. Mathematica Scandinavica 124 (2019) 15-33.
    14. [Links: journal, arxiv]
  14. Cosupport computations for finitely generated modules over commutative noetherian rings. Journal of Algebra 511 (2018) 249-269.
    15. [Links: journal, arxiv]
  15. Adams operations on matrix factorizations. Joint with M. Brown, C. Miller, and M. Walker. Algebra and Number Theory 11 (2017), No. 9, 2165-2192.
    16. [Links: journal, arxiv]
  16. Cyclic Adams operations. Joint with M. Brown, C. Miller, and M. Walker. Journal of Pure and Applied Algebra, Volume 221, Issue 7, July 2017, Pages 1589–1613.
    17. [Links: journal, arxiv]
  17. Stable Local Cohomology. Communications in Algebra, Issue 1, Vol 45, 2017.
    18. [Links: journal, arxiv]

Preprints (available for download)

  • The trace property in preenveloping classes. Joint with H. Lindo. Submitted.
    • [Links: arxiv]
  • Rigidity of Ext and Tor via flat–cotorsion theory. Joint with L. W. Christensen and L. Ferraro. Submitted.
    • [Links: arxiv]

About

My research is in algebra, with an emphasis on homological methods in commutative algebra. My interests also extend into algebraic K-theory, representation theory, triangulated categories, category theory, geometry, and topology. A motivating goal in my work is developing the relationship between properties of algebraic objects—such as rings or modules—and the structure of their resolutions.

You can watch a 5 minute video overview of my research that was recorded for the CHAMP seminar series in November 2020.

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From Peder's Ph.D. Defense talk, May 2016