Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The algebraic $K$-theory of the projective line associated with a
  strongly $\mathbb{Z}$-graded ring   A Laurent polynomial ring $A[t,1/t]$ with coefficients in a unital ring $A$
determines a category of quasi-coherent sheaves on the projective line over
$A$; its $K$-theory is known to split into a direct sum of two copies of the
$K$-theory of $A$. In this paper, the result is generalised to the case of an
arbitrary strongly $\mathbb{Z}$-graded ring $R$ in place of the Laurent
polynomial ring. The projective line associated with $R$ is indirectly defined
by specifying the corresponding category of quasi-coherent sheaves. Notions
from algebraic geometry like sheaf cohomology and twisting sheaves are
transferred to the new setting, and the $K$-theoretical splitting is
established.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
16
The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph