Geodesic
Endotrivial representations of finite groups and equivariant line bundles on the Brown complex
Balmer, Paul1
1 Mathematics Department, UCLA, Los Angeles, CA, United States
Geometry & topology, Tome 22 (2018) no. 7, pp. 4145-4161 Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

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We relate endotrivial representations of a finite group in characteristic p to equivariant line bundles on the simplicial complex of nontrivial p–subgroups, by means of weak homomorphisms.

DOI : 10.2140/gt.2018.22.4145
Classification : 20C20, 55P91
Keywords: endotrivial modules, line bundles, Brown complex, Brown Quillen complex of $p$–subgroups, weak homomorphism

Balmer, Paul 1

1 Mathematics Department, UCLA, Los Angeles, CA, United States 
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Balmer, Paul. Endotrivial representations of finite groups and equivariant line bundles on the Brown complex. Geometry & topology, Tome 22 (2018) no. 7, pp. 4145-4161. doi: 10.2140/gt.2018.22.4145

[1] P Balmer, Modular representations of finite groups with trivial restriction to Sylow subgroups, J. Eur. Math. Soc. 15 (2013) 2061 | DOI

[2] P Balmer, Stacks of group representations, J. Eur. Math. Soc. 17 (2015) 189 | DOI

[3] S Bouc, Homologie de certains ensembles ordonnés, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984) 49

[4] K S Brown, Euler characteristics of groups : the p–fractional part, Invent. Math. 29 (1975) 1 | DOI

[5] J F Carlson, N Mazza, D K Nakano, Endotrivial modules for the general linear group in a nondefining characteristic, Math. Z. 278 (2014) 901 | DOI

[6] J F Carlson, J Thévenaz, The classification of endo-trivial modules, Invent. Math. 158 (2004) 389 | DOI

[7] J F Carlson, J Thévenaz, The classification of torsion endo-trivial modules, Ann. of Math. 162 (2005) 823 | DOI

[8] J F Carlson, J Thévenaz, The torsion group of endotrivial modules, Algebra Number Theory 9 (2015) 749 | DOI

[9] V Guillemin, V Ginzburg, Y Karshon, Moment maps, cobordisms, and Hamiltonian group actions, 98, Amer. Math. Soc. (2002) | DOI

[10] A Hattori, T Yoshida, Lifting compact group actions in fiber bundles, Japan. J. Math. 2 (1976) 13 | DOI

[11] R Knörr, G R Robinson, Some remarks on a conjecture of Alperin, J. London Math. Soc. 39 (1989) 48 | DOI

[12] D Quillen, Homotopy properties of the poset of nontrivial p–subgroups of a group, Adv. in Math. 28 (1978) 101 | DOI

[13] G Segal, Equivariant K–theory, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 129 | DOI

[14] P Symonds, The orbit space of the p–subgroup complex is contractible, Comment. Math. Helv. 73 (1998) 400 | DOI

[15] J Thévenaz, Equivariant K–theory and Alperin’s conjecture, J. Pure Appl. Algebra 85 (1993) 185 | DOI

[16] J Thévenaz, P J Webb, Homotopy equivalence of posets with a group action, J. Combin. Theory Ser. A 56 (1991) 173 | DOI

[17] P J Webb, Subgroup complexes, from: "The Arcata conference on representations of finite groups" (editor P Fong), Proc. Sympos. Pure Math. 47, Amer. Math. Soc. (1987) 349

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