Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Hochschild cohomology and generalized Morita equivalence   We explore two constructions in homotopy category with algebraic precursors
in the theory of noncommutative rings and homological algebra, namely the
Hochschild cohomology of ring spectra and Morita theory. The present paper
provides an extension of the algebraic theory to include the case when $M$ is
not necessarily a progenerator. Our approach is complementary to recent work of
Dwyer and Greenlees and of Schwede and Shipley. A central notion of
noncommutative ring theory related to Morita equivalence is that of central
separable or Azumaya algebras. For such an Azumaya algebra A, its Hochschild
cohomology HH^*(A,A) is concentrated in degree 0 and is equal to the center of
A. We introduce a notion of topological Azumaya algebra and show that in the
case when the ground S-algebra R is an Eilenberg-Mac Lane spectrum of a
commutative ring this notion specializes to classical Azumaya algebras. A
canonical example of a topological Azumaya R-algebra is the endomorphism
R-algebra F_R(M,M) of a finite cell R-module. We show that the spectrum of mod
2 topological K-theory KU/2 is a nontrivial topological Azumaya algebra over
the 2-adic completion of the K-theory spectrum widehat{KU}_2. This leads to the
determination of THH(KU/2,KU/2), the topological Hochschild cohomology of KU/2.
As far as we know this is the first calculation of THH(A,A) for a
noncommutative S-algebra A.

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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an