Skip to main content

Spaces with Noetherian cohomology

  • Kasper K. S. Andersen (a1), Natàlia Castellana (a2), Vincent Franjou (a3), Alain Jeanneret (a4) and Jérôme Scherer (a5)...

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? In this paper we provide, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens–Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

Hide All
1.Adams, J. F., Stable homotopy and generalised homology, Chicago Lectures in Mathematics (University of Chicago Press, 1974).
2.Aguadé, J., Broto, C. and Notbohm, D., Homotopy classification of spaces with interesting cohomology and a conjecture of Cooke, I, Topology 33 (1994), 455492.
3.Andersen, K. K. S. and Grodal, J., The classification of 2-compact groups, J. Am. Math. Soc. 22(2) (2009), 387436.
4.Andersen, K. K. S., Grodal, J., Møller, J. M. and Viruel, A., The classification of p-compact groups for p odd, Annals Math. 167(1) (2008), 95210.
5.Atiyah, M. F. and Macdonald, I. G., Introduction to commutative algebra (Addison-Wesley, Reading, MA, 1969).
6.Benson, D. J. and Habegger, N., Varieties for modules and a problem of Steenrod, J. Pure Appl. Alg. 44 (1987), 1334.
7.Bousfield, A. K., On the p-adic completions of nonnilpotent spaces, Trans. Am. Math. Soc. 331(1) (1992), 335359.
8.Bousfield, A. K. and Kan, D. M., Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Volume 304 (Springer, 1972).
9.Broto, C., Levi, R. and Oliver, B., The homotopy theory of fusion systems, J. Am. Math. Soc. 16(4) (2003), 779856.
10.Brown, E. H. Jr, The cohomology of BSOn and BOn with integer coefficients, Proc. Am. Math. Soc. 85(2) (1982), 283288.
11.Čadek, M., The cohomology of BO(n) with twisted integer coefficients, J. Math. Kyoto Univ. 39(2) (1999), 277286.
12.Dwyer, W. G., Transfer maps for fibrations, Math. Proc. Camb. Phil. Soc. 120(2) (1996), 221235.
13.Dwyer, W. G. and Wilkerson, C. W., Homotopy fixed-point methods for Lie groups and finite loop spaces, Annals Math. 139(2) (1994), 395442.
14.Evens, L., The cohomology ring of a finite group, Trans. Am. Math. Soc. 101 (1961), 224239.
15.Evens, L., The spectral sequence of a finite group extension stops, Trans. Am. Math. Soc. 212 (1975), 269277.
16.Golod, E., The cohomology ring of a finite p-group, Dokl. Akad. Nauk SSSR 125 (1959), 703706.
17.Greenblatt, R., Homology with local coefficients and characteristic classes, Homol. Homot. Applic. 8(2) (2006), 91103.
18.Levi, R. and Ragnarsson, K., p-local finite group cohomology, Homol. Homot. Applic. 13(1) (2011), 223257.
19.Matsumura, H., Commutative ring theory, 2nd edn, Cambridge Studies in Advanced Mathematics, Volume 8 (Cambridge University Press, 1989).
20.Minh, P. A. and Symonds, P., Cohomology and finite subgroups of profinite subgroups, Proc. Am. Math. Soc. 132(6) (2004), 15811588.
21.Moerdijk, I. and Svensson, J.-A., The equivariant Serre spectral sequence, Proc. Am. Math. Soc. 118(1) (1993), 263278.
22.Møller, J. M., N-determined 2-compact groups, II, Fund. Math. 196(1) (2007), 190.
23.Ragnarsson, K., Classifying spectra of saturated fusion systems, Alg. Geom. Topol. 6 (2006), 195252.
24.Spanier, E. H., Algebraic topology (Springer, 1981; corrected reprint).
25.Venkov, B. B., Cohomology algebras for some classifying spaces, Dokl. Akad. Nauk SSSR 127 (1959), 943944.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed