Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Controlled Algebra for Simplicial Rings and Algebraic K-theory   We develop a version of controlled algebra for simplicial rings. This
generalizes the methods which lead to successful proofs of the algebraic K-
theory isomorphism conjecture (Farrell-Jones Conjecture) for a large class of
groups. This is the first step to prove the algebraic K-theory isomorphism
conjecture for simplicial rings. We construct a category of controlled
simplicial modules, show that it has the structure of a Waldhausen category and
discuss its algebraic K-theory.
  We lay emphasis on detailed proofs. Highlights include the discussion of a
simplicial cylinder functor, the gluing lemma, a simplicial mapping telescope
to split coherent homotopy idempotents, and a direct proof that a weak
equivalence of simplicial rings induces an equivalence on their algebraic
K-theory. Because we need a certain cofinality theorem for algebraic K-theory,
we provide a proof and show that a certain assumption, sometimes omitted in the
literature, is necessary. Last, we remark how our setup relates to ring
spectra.

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The categories of this paper are: cs
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga