Geodesic
The Equivariant Generating Hypothesis
Bohmann, Anna Marie1
1Department of Mathematics, University of Chicago, Chicago IL 60637, USA
Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 1003-1016
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We state the generating hypothesis in the homotopy category of G–spectra for a compact Lie group G and prove that if G is finite, then the generating hypothesis implies the strong generating hypothesis, just as in the non-equivariant case. We also give an explicit counterexample to the generating hypothesis in the category of rational S1–equivariant spectra.

DOI : 10.2140/agt.2010.10.1003
Keywords: generating hypothesis, Freyd conjecture, equivariant stable homotopy

Bohmann, Anna Marie  1

1 Department of Mathematics, University of Chicago, Chicago IL 60637, USA 
@article{10_2140_agt_2010_10_1003,
     author = {Bohmann, Anna Marie},
     title = {The {Equivariant} {Generating} {Hypothesis}},
     journal = {Algebraic and Geometric Topology},
     pages = {1003--1016},
     year = {2010},
     volume = {10},
     number = {2},
     doi = {10.2140/agt.2010.10.1003},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.1003/}
}
TY  - JOUR
AU  - Bohmann, Anna Marie
TI  - The Equivariant Generating Hypothesis
JO  - Algebraic and Geometric Topology
PY  - 2010
SP  - 1003
EP  - 1016
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.1003/
DO  - 10.2140/agt.2010.10.1003
ID  - 10_2140_agt_2010_10_1003
ER  - 
%0 Journal Article
%A Bohmann, Anna Marie
%T The Equivariant Generating Hypothesis
%J Algebraic and Geometric Topology
%D 2010
%P 1003-1016
%V 10
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.1003/
%R 10.2140/agt.2010.10.1003
%F 10_2140_agt_2010_10_1003
Bohmann, Anna Marie. The Equivariant Generating Hypothesis. Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 1003-1016. doi: 10.2140/agt.2010.10.1003

[1] D J Benson, S K Chebolu, J D Christensen, J Mináč, The generating hypothesis for the stable module category of a $p$–group, J. Algebra 310 (2007) 428

[2] J F Carlson, S K Chebolu, J Mináč, Freyd's generating hypothesis with almost split sequences, Proc. Amer. Math. Soc. 137 (2009) 2575

[3] A W M Dress, Contributions to the theory of induced representations, from: "Algebraic $K$–theory, II: “Classical” algebraic $K$–theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)", Springer (1973)

[4] P Freyd, Stable homotopy, from: "Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965)", Springer (1966) 121

[5] J P C Greenlees, Rational $S^1$–equivariant stable homotopy theory, Mem. Amer. Math. Soc. 138 (1999)

[6] J P C Greenlees, J P May, Generalized Tate cohomology, Mem. Amer. Math. Soc. 113 (1995)

[7] M Hovey, K Lockridge, G Puninski, The generating hypothesis in the derived category of a ring, Math. Z. 256 (2007) 789

[8] I Kříž, J P May, Operads, algebras, modules and motives, Astérisque (1995)

[9] L G Lewis Jr., J P May, M Steinberger, J E Mcclure, Equivariant stable homotopy theory, Lecture Notes in Mathematics 1213, Springer (1986)

[10] K H Lockridge, The generating hypothesis in the derived category of $R$–modules, J. Pure Appl. Algebra 208 (2007) 485

[11] A Neeman, Triangulated categories, Annals of Mathematics Studies 148, Princeton University Press (2001)

Cité par Sources :