leuschke.org




Research/Papers in Commutative Algebra

This is a project in its very early stages.

What I’d like to do here is compile a list of papers that
(a) I can point a grad student to when s/he asks “What should I read”,
(b) is available on the web, either via the ArXiv or JStor, etc.,
(c) show that reading “old” papers can still be incredibly valuable to current researchers, and/or
(d) have influenced my own personal view of what commutative algebra is.
For now, these will all be in English — I’m particularly interested in hunting up English translations of old papers from Hilbert, Krull, Noether, etc. When I get back around to this, there will be PDFs available for download (as long as I can reconcile that with copyright).

The following are off the top of my head. You’re welcome to add things (click “Comment”, down there at the bottom and I’ll add them for you — eventually I’ll get this all set up so you can add things without my help). Also, there will eventually be a separate list for expository papers, so feel free to suggest excellent examples of such.

  • Auslander’s “Modules over unramified regular local rings” and “Purity of the branch locus” and Auslander-Buchsbaum on homological dimensions
  • Eisenbud’s 1980 paper on resolutions over complete intersections, with the theory of matrix factorizations
  • Heitmann’s example of a non-rigid module
  • Eagon and Hochster’s paper on generic perfection
  • Miyata’s paper on extensions
  • Abhyankar, “Local rings of high embedding dimension”
  • Bass’s Ubiquity paper
  • Mac Lane, “Duality for Groups” (I only include this 1950 paper for the footnote on page 486: “Call the dual [in this sense] of a free [nonabelian] group a fascist group. R. Baer has shown me a proof of the elegant theorem: Every fascist group consists only of the identity element.”)
  • Peskine—Szpiro