Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Segal's Gamma rings and universal arithmetic   Segal's Gamma-rings provide a natural framework for absolute algebraic
geometry. We use Almkvist's global Witt construction to explore the relation
with J. Borger F1-geometry and compute the Witt functor-ring of Almkvist for
the simplest Gamma-ring S. We prove that it is isomorphic to the Galois
invariant part of the BC-system, and exhibit the close relation between
Lambda-rings and the Arithmetic site. Then, we concentrate on the Arakelov
compactification of Z which acquires a structure sheaf of S-algebras. After
supplying a probabilistic interpretation of the classical theta invariant of a
divisor D, we show how to associate to D a Gamma-space that encodes, in
homotopical terms, the Riemann-Roch problem for D.

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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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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: q-fin