# Mark Hovey's papers

Here are Mark Hovey's publications, in reverse chronological order.

1. Smith ideals of structured ring spectra , submitted version. Abstract, Pdf.

2. Brown representability and the Eilenberg-Watts theorem in homotopical algebra , (2013 version of older preprint), submitted version. Abstract, Pdf.

3. Quillen model categories , Journal of K-theory 11 (2013), 469--478. Abstract, Pdf.

4. Homological dimensions of ring spectra , with Keir Lockridge, Homology, Homotopy, and Applications 15 (2013), 53--71. Abstract, Pdf.

5. The ghost and weak dimensions of rings and ring spectra, with Keir Lockridge, Israel J. Math. 182 (2011), 31--46. Abstract, Pdf.

6. Additive closed symmetric monoidal structures on R-modules, J. Pure Appl. Algebra 215 (2011), 789--805. Abstract, Pdf.

7. Gorenstein model structures and generalized derived categories, with James Gillespie, Proc. Edinb. Math. Soc. (2) 53 (2010), 675--696. Abstract, Pdf.

8. Intersection homological algebra, New topological contexts for Galois theory and algebraic geometry, 133--150, Geom. Topol. Monogr., 16 , Geom. Topol. Publ., Coventry, (2009). Abstract, Pdf.

9. Bounds on the distinguishing chromatic number, with Karen L. Collins and Ann N. Trenk, Electron. J. Combin. 16 (2009), no. 1, Research Paper 88, 14 pp. Abstract, Pdf.

10. Semisimple ring spectra, with Keir Lockridge, New York J. Math. 15 (2009), 219--243. Abstract, Pdf.

11. The ghost dimension of a ring, with Keir Lockridge, Proc. Amer. Math. Soc. 137 (2009), 1907--1913. Abstract, Pdf.

12. The homotopy of $MString$ and $MU \langle 6 \rangle$ at large primes, Algebr. Geom. Topol. 8 (2008), 2401--2414. Abstract, Pdf.

13. Morava $E$-theory of filtered colimits, Trans. Amer. Math. Soc. 360 (2008), 369--382. Abstract, Dvi, Pdf.

14. Cotorsion pairs and model categories, Interactions between homotopy theory and algebra, 277--296, Contemp. Math. 436, Amer. Math. Soc., Providence, RI, 2007. Abstract, Dvi, Pdf.

15. Injective comodules and Landweber exact homology theories, Fund. Math. 196 (2007), 237--251. Abstract, Dvi, Pdf.

16. On Freyd's generating hypothesis, Q. J. Math. 58 (2007), 31--45. Abstract, Dvi, Pdf.

17. The generating hypothesis in the derived category of a ring, with Keir Lockridge and Gena Puninski, Math. Z. 256 (2007), 789--800. Abstract, Pdf.

18. The generalized homology of products, Glasg. Math. J. 49 (2007), 1--10. Abstract, Dvi, Pdf.

19. Chromatic phenomena in the algebra of BP*BP-comodules, Elliptic cohomology: geometry, applications, and higher chromatic analogues, 170--203, London Math. Soc. Lecture Notes {342}, Cambridge University Press, Cambridge, 2007. Abstract, Dvi, Pdf.

20. Local cohomology of BP*BP-comodules, with Neil Strickland, Proc. London Math. Soc. (3) 90 (2005) 521--544. Abstract, Dvi, Pdf.

21. Comodules and Landweber exact homology theories, with Neil Strickland, Adv. Math. 192 (2005), 427--456. Abstract, Dvi, Pdf.

22. Operations and co-operations in Morava E-theory, Homology Homotopy Appl. 6 (2004), 201--236. Abstract, Dvi, Pdf.

23. Homotopy theory of comodules over a Hopf algebroid, Homotopy theory: relations with algebraic geometry, group cohomology and algebraic $K$-theory (Evanston, IL 2002), 261--304, Contemp. Math. 346, Amer. Math. Soc., Providence, RI, 2004. Abstract, Dvi, Pdf.

24. Morita theory for Hopf algebroids and presheaves of groupoids, Amer. J. Math. 124 (2002), 1289-1318. Abstract, Dvi.

25. Cotorsion pairs, model category structures, and representation theory, Math. Z. 241 (2002), 553-592. Abstract, Dvi.

26. Quillen model structures for relative homological algebra, with J. Daniel Christensen, Math. Proc. Camb. Phil. Soc. 133 (2002), 261-293. Abstract, Dvi.

27. Spectra and symmetric spectra in general model categories, J. Pure Appl. Alg. 165 (2001), 63-127. Abstract, Dvi.

28. Classifying subcategories of modules, Trans. Amer. Math. Soc., 353 (2001), 3181-3191. Abstract, Dvi. Note that this paper also has an erratum, which appeared in Trans. Amer. Math. Soc. 360 (2008), p. 2809. Here is the Pdf.

29. Stably thick subcategories of modules over Hopf algebras, with John Palmieri, Math. Proc. Camb. Phil. Soc. 130 (2001), 441-474. Abstract, Dvi .

30. Model category structures on chain complexes of sheaves, Transactions of the AMS 353 (2001), 2441-2457. Abstract, Dvi .

31. Galois theory of thick subcategories in modular representation theory, with John Palmieri, J. Algebra , 230 (2000), 713-729. Abstract, Dvi .

32. Phantom maps and chromatic phantom maps, with J. Daniel Christensen, Amer. J. Math., 122 (2000), 275--293. Abstract, Dvi.

33. Symmetric spectra, with Brooke Shipley and Jeff Smith, J. Amer. Math. Soc. 13 (2000), no. 1, 149--208. The most sensible thing you can do here is go to the Journal's web site, where you ought to be able to download the published version. If not, Abstract, Dvi .

34. Invertible spectra in the E(n)-local stable homotopy category, with Hal Sadofsky, J. London Math. Soc. (2) 60 (1999), 284--302. Abstract, Dvi, Ps, .

35. The structure of the Bousfield lattice, with John Palmieri, Homotopy invariant algebraic structures (Baltimore, MD 1998), 175--196, Contemp. Math. 239, Amer. Math. Soc., Providence, RI, 1999. Abstract, Dvi.

36. Model categories, Mathematical Surveys and Monographs 63, AMS, Providence, RI, 1999 (x + 209 pages). This book has now appeared, so I will no longer let you download it. You can look at the table of contents. Also, I am keeping a list of errata, in hopes of a second edition and in the interests of accuracy, so if you know of any, please send them to me. Here is the .dvi file of errata, last modified 5/2/2002.

37. Morava K-theories and localisation, with Neil Strickland, Mem. Amer. Math. Soc. 139, no. 666 (1999) (104 pages). Dvi, Ps, Abstract.

38. v_n-Elements in ring spectra and applications to bordism theory, Duke Mathematical Journal, 88 (1997), 327-356. Abstract, Dvi, Ps.

39. Axiomatic stable homotopy theory, with John Palmieri and Neil Strickland, Mem. Amer. Math. Soc. , 128, no. 610 (1997) (114 pages). Abstract, Dvi, Ps.

40. Tate cohomology lowers chromatic Bousfield classes, with Hal Sadofsky, Proceedings of the American mathematical Society, 124 (1996), 3579-3585. Abstract, Dvi, Ps.

41. Cohomological Bousfield classes, Journal of Pure and Applied Algebra, 103, (1995), 45-59. Abstract, Dvi, Ps.

42. Spin bordism and elliptic homology, Matematische Zeitschrift, 219, (1995), 163-170. Abstract, Dvi, Ps.

43. Bousfield localization functors and Hopkins' chromatic splitting conjecture, The Cech Centennial (M. Cenkl and H. Miller, eds.), Contemporary Mathematics, volume 181, American Mathematical Society, 1995, pp. 225-250. Abstract, Dvi, Ps.

44. The 7-connected cobordism ring at p=3, with Doug Ravenel, Transactions of the American Mathematical Society, 347, (1995), 3473-3502. Abstract, Dvi, Ps.

45. Lusternik-Schnirelmann cocategory, Illinois Journal of Mathematics 37 (1993), 224-239. Abstract, Dvi, Ps.

46. A proof of the existence of level one elliptic cohomology, Proceedings of the American Mathematical Society 118 (1993) 1331-1334. Abstract, Dvi, Ps.

47. Spin cobordism determines real K-theory, with Mike Hopkins, Mathematische Zeitschrift, 210 (1992), 181-196. Abstract, Dvi, Ps.

48. A-cordial graphs, Discrete Mathematics 93 (1991), 183-194.

49. A bijective proof for the parity of Stirling numbers, with Karen Collins, Ars Combinatoria 31 (1991), 31-32.

50. Most graphs are edge-cordial, with Karen Collins Ars Combinatoria 30 (1990), 289-295.
Here are a couple of unpublished items that might be useful as well.
1. Some spectral sequences in Morava E-theory, (35 pages). This paper will never be published in this form, but I leave it here because it is essentially an encyclopedia of spectral sequences in Morava E-theory, so might be useful as a reference, at least for myself. I took the spectral sequence that was really new in this paper and put it into the paper "Morava E-theory is n-1 derived functors away from a homology theory". Abstract, Dvi, Pdf.
2. Monoidal model categories, preprint, 14 pages, (1998) This paper will never be published, but it did mark the introduction of what are now called "semi-model categories". The issue is that if you have a triple T on a model category, the category of T-algebras is often not a model category, but it does retain a significant amount of the model category structure. This later became important in work of Markus Spitzweck, among others. I therefore include it here for historical purposes. Abstract, Dvi, or Pdf.