Classifying subcategories of modules
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- by Mark Hovey PDF
- Trans. Amer. Math. Soc. 353 (2001), 3181-3191 Request permission
Erratum: Trans. Amer. Math. Soc. 360 (2008), 2809-2809.
Abstract:Let $R$ be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented $R$-modules that are closed under extensions. We also classify abelian subcategories of arbitrary $R$-modules that are closed under extensions and coproducts, when $R$ is commutative and Noetherian. The method relies on comparison with the derived category of $R$.
- J. Daniel Christensen, Bernhard Keller, and Amnon Neeman, Failure of Brown representability in derived categories, preprint, 1999.
- Sarah Glaz, Commutative coherent rings, Lecture Notes in Mathematics, vol. 1371, Springer-Verlag, Berlin, 1989. MR 999133, DOI 10.1007/BFb0084570
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Michael J. Hopkins, Global methods in homotopy theory, Homotopy theory (Durham, 1985) London Math. Soc. Lecture Note Ser., vol. 117, Cambridge Univ. Press, Cambridge, 1987, pp. 73–96. MR 932260
- Mark Hovey, Model categories, Mathematical Surveys and Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999. MR 1650134
- Mark Hovey and John H. Palmieri, Stably thick subcategories of modules over Hopf algebras, to appear in Math. Proc. Camb. Phil. Soc.
- Mark Hovey and John H. Palmieri, Galois theory of thick subcategories in modular representation theory, J. Algebra 230 (2000), 713–729.
- Mark Hovey, John H. Palmieri, and Neil P. Strickland, Axiomatic stable homotopy theory, Mem. Amer. Math. Soc. 128 (1997), no. 610, x+114. MR 1388895, DOI 10.1090/memo/0610
- Michael J. Hopkins and Jeffrey H. Smith, Nilpotence and stable homotopy theory. II, Ann. of Math. (2) 148 (1998), no. 1, 1–49. MR 1652975, DOI 10.2307/120991
- Amnon Neeman, The chromatic tower for $D(R)$, Topology 31 (1992), no. 3, 519–532. With an appendix by Marcel Bökstedt. MR 1174255, DOI 10.1016/0040-9383(92)90047-L
- Bo Stenström, Rings of quotients, Die Grundlehren der mathematischen Wissenschaften, Band 217, Springer-Verlag, New York-Heidelberg, 1975. An introduction to methods of ring theory. MR 0389953
- R. W. Thomason, The classification of triangulated subcategories, Compositio Math. 105 (1997), no. 1, 1–27. MR 1436741, DOI 10.1023/A:1017932514274
- Mark Hovey
- Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
- Email: email@example.com
- Received by editor(s): January 15, 2000
- Received by editor(s) in revised form: June 19, 2000
- Published electronically: April 12, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 3181-3191
- MSC (2000): Primary 13C05, 18E30, 18G35
- DOI: https://doi.org/10.1090/S0002-9947-01-02747-7
- MathSciNet review: 1828603