On finite resolutions of K(n)-local spheres

Hans-Werner Henn (1)

1 IRMA - Institut de Recherche Mathématique Avancée

For odd primes $p$ we construct finite resolutions of the trivial module $_p$ for the $n$-th Morava stabilizer groupby (direct summands of) permutationmodules with respect to finite $p$-subgroups.Furthermore we discussthe problem of realizing these resolutionsby finite resolutions of the $K(n)$-local sphere byspectra which are (direct summands of)wedges of homotopy fixed point spectrafor the action of these finite $p$-subgroupson the Lubin-Tate spectrum $E_n$.

Mots clés: Stable homotopy theory; K(n)-localization; "Stable homotopy theory; K(n)-localization"

Domaines: Topologie algébrique [math.AT]

Hans-Werner Henn. On finite resolutions of K(n)-local spheres. Elliptic Cohomology : Geometry, Applications, and Higher Chromatic Analogues, 2007, ⟨10.1017/CBO9780511721489.008⟩. ⟨hal-00129702⟩