Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy fixed points for profinite groups emulate homotopy fixed points
  for discrete groups   If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point
spectrum Z^{hK} is Map_*(EK_+, Z)^K, the fixed points of a familiar expression.
Similarly, if G is a profinite group and X is a discrete G-spectrum, then
X^{hG} is often given by (H_{G,X})^G, where H_{G,X} is a certain explicit
construction given by a homotopy limit in the category of discrete G-spectra.
Thus, in each of two common equivariant settings, the homotopy fixed point
spectrum is equal to the fixed points of an explicit object in the ambient
equivariant category. We enrich this pattern by proving in a precise sense that
the discrete G-spectrum H_{G,X} is just "a profinite version" of Map_*(EK_+,
Z): at each stage of its construction, H_{G,X} replicates in the setting of
discrete G-spectra the corresponding stage in the formation of Map_*(EK_+, Z)
(up to a certain natural identification).

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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an