Duke Mathematical Journal

Nilpotence for modules over the $\mod 2$ Steenrod algebra, I

John H. Palmieri
Source: Duke Math. J. Volume 82, Number 1 (1996), 195-208.
First Page: Show Hide

Related Works:

Primary Subjects: 55S10
Secondary Subjects: 18G15, 55P42
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077244844
Mathematical Reviews number (MathSciNet): MR1387226
Zentralblatt MATH identifier: 0876.55012
Digital Object Identifier: doi:10.1215/S0012-7094-96-08208-3

References

[1] D. W. Anderson and D. M. Davis, A vanishing theorem in homological algebra, Comment. Math. Helv. 48 (1973), 318–327.
Mathematical Reviews (MathSciNet): MR48:12526
Zentralblatt MATH: 0267.55022
Digital Object Identifier: doi:10.1007/BF02566125
[2]1 D. J. Benson, Representations and cohomology. I, Cambridge Studies in Advanced Mathematics, vol. 30, Cambridge University Press, Cambridge, 1991.
Mathematical Reviews (MathSciNet): MR92m:20005
Zentralblatt MATH: 0718.20001
[2]2 D. J. Benson, Representations and cohomology. II, Cambridge Studies in Advanced Mathematics, vol. 31, Cambridge University Press, Cambridge, 1991.
Mathematical Reviews (MathSciNet): MR93g:20099
Zentralblatt MATH: 0731.20001
[3] J. F. Carlson, Complexity and Krull dimension, Representations of algebras (Puebla, 1980), Lecture Notes in Math., vol. 903, Springer, Berlin, 1981, pp. 62–67.
Mathematical Reviews (MathSciNet): MR83h:16033
Zentralblatt MATH: 0475.20040
[4] E. S. Devinatz, M. J. Hopkins, and J. H. Smith, Nilpotence and stable homotopy theory. I, Ann. of Math. (2) 128 (1988), no. 2, 207–241.
Mathematical Reviews (MathSciNet): MR89m:55009
Zentralblatt MATH: 0673.55008
Digital Object Identifier: doi:10.2307/1971440
[5] M. 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.
Mathematical Reviews (MathSciNet): MR89g:55022
Zentralblatt MATH: 0657.55008
[6] M. J. Hopkins and J. H. Palmieri, A nilpotence theorem for modules over the mod $2$ Steenrod algebra, Topology 32 (1993), no. 4, 751–756.
Mathematical Reviews (MathSciNet): MR94f:55014
Zentralblatt MATH: 0801.55011
Digital Object Identifier: doi:10.1016/0040-9383(93)90049-2
[7] M. J. Hopkins and D. C. Ravenel, A proof of the smash product conjecture, preprint.
[8] M. J. Hopkins and J. H. Smith, Nilpotence and stable homotopy theory II, preprint.
Mathematical Reviews (MathSciNet): MR1652975
Zentralblatt MATH: 0927.55015
Digital Object Identifier: doi:10.2307/120991
[9]1 W. H. Lin, Cohomology of sub-Hopf-algebras of the Steenrod algebra, J. Pure Appl. Algebra 10 (1977/78), no. 2, 101–113.
Mathematical Reviews (MathSciNet): MR56:13217
Zentralblatt MATH: 0378.55011
Digital Object Identifier: doi:10.1016/0022-4049(77)90013-5
[9]2 W. H. Lin, Cohomology of sub-Hopf-algebras of the Steenrod algebra. II, J. Pure Appl. Algebra 11 (1977/78), no. 1-3, 105–110.
Mathematical Reviews (MathSciNet): MR58:22249
Zentralblatt MATH: 0441.55015
Digital Object Identifier: doi:10.1016/0022-4049(77)90045-7
[10] M. Mahowald and H. Sadofsky, $v\sb n$ telescopes and the Adams spectral sequence, Duke Math. J. 78 (1995), no. 1, 101–129.
Mathematical Reviews (MathSciNet): MR96h:55006
Zentralblatt MATH: 0984.55008
Digital Object Identifier: doi:10.1215/S0012-7094-95-07806-5
Project Euclid: euclid.dmj/1077285551
[11] H. R. Margolis, Spectra and the Steenrod algebra, North-Holland Mathematical Library, vol. 29, North-Holland Publishing Co., Amsterdam, 1983.
Mathematical Reviews (MathSciNet): MR86j:55001
Zentralblatt MATH: 0552.55002
[12] H. R. Miller and C. Wilkerson, Vanishing lines for modules over the Steenrod algebra, J. Pure Appl. Algebra 22 (1981), no. 3, 293–307.
Mathematical Reviews (MathSciNet): MR82m:55024
Zentralblatt MATH: 0469.55012
Digital Object Identifier: doi:10.1016/0022-4049(81)90104-3
[13] J. W. Milnor, The Steenrod algebra and its dual, Ann. of Math. (2) 67 (1958), 150–171.
Mathematical Reviews (MathSciNet): MR20:6092
Zentralblatt MATH: 0080.38003
Digital Object Identifier: doi:10.2307/1969932
[14] J. W. Milnor and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211–264.
Mathematical Reviews (MathSciNet): MR30:4259
Zentralblatt MATH: 0163.28202
Digital Object Identifier: doi:10.2307/1970615
[15] G. Nishida, The nilpotency of elements of the stable homotopy groups of spheres, J. Math. Soc. Japan 25 (1973), 707–732.
Mathematical Reviews (MathSciNet): MR49:6236
Zentralblatt MATH: 0261.55013
Digital Object Identifier: doi:10.2969/jmsj/02540707
Project Euclid: euclid.jmsj/1240435467
[16] J. H. Palmieri, The chromatic filtration and the Steenrod algebra, Topology and representation theory (Evanston, IL, 1992) eds. E. M. Friedlander and M. E. Mahowald, Contemp. Math., vol. 158, Amer. Math. Soc., Providence, RI, 1994, pp. 187–201.
Mathematical Reviews (MathSciNet): MR95d:55016
Zentralblatt MATH: 0797.55012
[17] J. H. Palmieri, Nilpotence for modules over the mod $2$ Steenrod algebra. I, II, Duke Math. J. 82 (1996), no. 1, 195–208, 209–226.
Mathematical Reviews (MathSciNet): MR97c:55028
Zentralblatt MATH: 0876.55013
Digital Object Identifier: doi:10.1215/S0012-7094-96-08208-3
Project Euclid: euclid.dmj/1077244844
[18] J. H. Palmieri and H. Sadofsky, Self-maps of spectra, a theorem of J. Smith, and Margolis' killing construction, Math. Z. 215 (1994), no. 3, 477–490.
Mathematical Reviews (MathSciNet): MR94k:55016
Zentralblatt MATH: 0792.55005
Digital Object Identifier: doi:10.1007/BF02571725
[19] D. C. Ravenel, Life after the telescope conjecture, preprint.
Mathematical Reviews (MathSciNet): MR1367299
Zentralblatt MATH: 0899.55009
[20] D. C. Ravenel, Nilpotence and periodicity in stable homotopy theory, Annals of Mathematics Studies, vol. 128, Princeton University Press, Princeton, NJ, 1992.
Mathematical Reviews (MathSciNet): MR94b:55015
Zentralblatt MATH: 0774.55001
[21] C. Wilkerson, The cohomology algebras of finite-dimensional Hopf algebras, Trans. Amer. Math. Soc. 264 (1981), no. 1, 137–150.
Mathematical Reviews (MathSciNet): MR82e:16019
Zentralblatt MATH: 0465.55010
Digital Object Identifier: doi:10.2307/1998415

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?