Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tate cohomology and periodic localization of polynomial functors   In this paper, we show that Goodwillie calculus, as applied to functors from
stable homotopy to itself, interacts in striking ways with chromatic aspects of
the stable category.
  Localized at a fixed prime p, let T(n) be the telescope of a v_n self map of
a finite S--module of type n. The Periodicity Theorem of Hopkins and Smith
implies that the Bousfield localization functor associated to T(n) is
independent of choices.
  Goodwillie's general theory says that to any homotopy functor F from
S--modules to S--modules, there is an associated tower under F, {P_dF}, such
that F --> P_dF is the universal arrow to a d--excisive functor.
  Our first theorem says that P_dF --> P_{d-1}F always admits a homotopy
section after localization with respect to T(n) (and so also after localization
with respect to Morava K--theory K(n)). Thus, after periodic localization,
polynomial functors split as the product of their homogeneous factors.
  This theorem follows from our second theorem which is equivalent to the
following: for any finite group G, the Tate spectrum t_G(T(n)) is weakly
contractible. This strengthens and extends previous theorems of
Greenlees--Sadofsky, Hovey--Sadofsky, and Mahowald--Shick. The Periodicity
Theorem is used in an essential way in our proof.
  The connection between the two theorems is via a reformulation of a result of
McCarthy on dual calculus.

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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: funct-an