Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chromatic splitting for the $K(2)$-local sphere at $p=2$   We calculate the homotopy type of $L_1L_{K(2)}S^0$ and $L_{K(1)}L_{K(2)}S^0$
at the prime 2, where $L_{K(n)}$ is localization with respect to Morava
$K$-theory and $L_1$ localization with respect to $2$-local $K$ theory. In
$L_1L_{K(2)}S^0$ we find all the summands predicted by the Chromatic Splitting
Conjecture, but we find some extra summands as well. An essential ingredient in
our approach is the analysis of the continuous group cohomology
$H^\ast_c(\mathbb{G}_2,E_0)$ where $\mathbb{G}_2$ is the Morava stabilizer
group and $E_0 = \mathbb{W}[[u_1]]$ is the ring of functions on the height $2$
Lubin-Tate space. We show that the inclusion of the constants $\mathbb{W} \to
E_0$ induces an isomorphism on group cohomology, a radical simplification.

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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: econ