Publikationsdatum:
2011-11-24
Beschreibung:
Let G be a profinite group, { X α } α be a cofiltered diagram of discrete G -spectra, and Z be a spectrum with trivial G -action. We show how to define the homotopy fixed point spectrum F ( Z , holim α X α ) hG and that when G has finite virtual cohomological dimension (vcd), it is equivalent to F ( Z , holim α ( X α ) hG ). With these tools, we show that the K ( n )-local Spanier–Whitehead dual is always a homotopy fixed point spectrum, a well-known Adams-type spectral sequence is actually a descent spectral sequence, and, for a sufficiently nice k -local profinite G -Galois extension E , with K G and closed, the equivalence (due to Behrens and the author), where denotes k -local homotopy fixed points, can be upgraded to an equivalence that just uses ordinary ( non-local ) homotopy fixed points, when G / K has finite vcd.
Print ISSN:
0024-6093
Digitale ISSN:
1469-2120
Thema:
Mathematik
Permalink
