Function spectra and continuous G-spectra

Let G be a profinite group, {X_alpha}_alpha a cofiltered diagram of discrete G-spectra, and Z a spectrum with trivial G-action. We show how to define the homotopy fixed point spectrum F(Z, holim_alpha X_alpha)^{hG} and that when G has finite virtual cohomological dimension (vcd), it is equivalent to F(Z, holim_alpha (X_alpha)^{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 a closed normal subgroup of G, the equivalence (E^{h_kK})^{h_kG/K} \simeq E^{h_kG} (due to Behrens and the author), where (-)^{h_k(-)} 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.Comment: submitted for publicatio

The homotopy orbit spectrum for profinite groups

Let G be a profinite group. We define an S[[G]]-module to be a G-spectrum X that satisfies certain conditions, and, given an S[[G]]-module X, we define the homotopy orbit spectrum X_{hG}. When G is countably based and X satisfies a certain finiteness condition, we construct a homotopy orbit spectral sequence whose E_2-term is the continuous homology of G with coefficients in the graded profinite $\hat{\mathbb{Z}}[[G]]$-module $\pi_\ast(X)$. Let G_n be the extended Morava stabilizer group and let E_n be the Lubin-Tate spectrum. As an application of our theory, we show that the function spectrum F(E_n,L_{K(n)}(S^0)) is an S[[G_n]]-module with an associated homotopy orbit spectral sequence.Comment: 13 page

Social norms and human normative psychology

Our primary aim in this paper is to sketch a cognitive evolutionary approach for developing explanations of social change that is anchored on the psychological mechanisms underlying normative cognition and the transmission of social norms. We throw the relevant features of this approach into relief by comparing it with the self-fulfilling social expectations account developed by Bicchieri and colleagues. After describing both accounts, we argue that the two approaches are largely compatible, but that the cognitive evolutionary approach is well- suited to encompass much of the social expectations view, whose focus on a narrow range of norms comes at the expense of the breadth the cognitive evolutionary approach can provide

The homotopy fixed point spectra of profinite Galois extensions

Let E be a k-local profinite G-Galois extension of an E_infty-ring spectrum A (in the sense of Rognes). We show that E may be regarded as producing a discrete G-spectrum. Also, we prove that if E is a profaithful k-local profinite extension which satisfies certain extra conditions, then the forward direction of Rognes's Galois correspondence extends to the profinite setting. We show the function spectrum F_A((E^hH)_k, (E^hK)_k) is equivalent to the homotopy fixed point spectrum ((E[[G/H]])^hK)_k where H and K are closed subgroups of G. Applications to Morava E-theory are given, including showing that the homotopy fixed points defined by Devinatz and Hopkins for closed subgroups of the extended Morava stabilizer group agree with those defined with respect to a continuous action and in terms of the derived functor of fixed points.Comment: 60 Page

How much has house lock affected labor mobility and the unemployment rate?

This article explores new evidence from the U.S. Census Bureau’s Survey of Income and Program Participation (SIPP) on the extent to which “house lock”--the reluctance of households to sell their homes in a declining house price environment--has contributed to the elevated unemployment rate since 2008.Labor policy ; Unemployment