On cyclic fixed points of spectra
Abstract
For a finite pgroup G and a bounded below Gspectrum X of finite type mod p, the Gequivariant Segal conjecture for X asserts that the canonical map X^G > X^{hG} is a padic equivalence. Let C_{p^n} be the cyclic group of order p^n. We show that if the C_p Segal conjecture holds for a C_{p^n} spectrum X, as well as for each of its C_{p^e} geometric fixed points for 0 < e < n, then then C_{p^n} Segal conjecture holds for X. Similar results hold for weaker forms of the Segal conjecture, asking only that the canonical map induces an equivalence in sufficiently high degrees, on homotopy groups with suitable finite coefficients.
 Publication:

arXiv eprints
 Pub Date:
 December 2007
 DOI:
 10.48550/arXiv.0712.3476
 arXiv:
 arXiv:0712.3476
 Bibcode:
 2007arXiv0712.3476B
 Keywords:

 Mathematics  Algebraic Topology;
 55P91
 EPrint:
 Mathematische Zeitschrift 276 (2014) 8191