Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A blueprinted view on $\mathbb F_1$-geometry   This overview paper has two parts. In the first part, we review the
development of $\mathbb F_1$-geometry from the first mentioning by Jacques Tits
in 1956 until the present day. We explain the main ideas around $\mathbb F_1$,
embedded into the historical context, and give an impression of the multiple
connections of $\mathbb F_1$-geometry to other areas of mathematics.
  In the second part, we review (and preview) the geometry of blueprints.
Beyond the basic definitions of blueprints, blue schemes and projective
geometry, this includes a theory of Chevalley groups over $\mathbb F_1$
together with their action on buildings over $\mathbb F_1$; computations of the
Euler characteristic in terms of $\mathbb F_1$-rational points, which involve
quiver Grassmannians; $K$-theory of blue schemes that reproduces the formula
$K_i(\mathbb F_1)=\pi^{st}_i(S^0)$; models of the compactifications of $\Spec
\mathbb Z$ and other arithmetic curves; and explanations about the connections
to other approaches towards $\mathbb F_1$ like monoidal schemes after Deitmar,
$B_1$-algebras after Lescot, $\Lambda$-schemes after Borger, relative schemes
after To\"en and Vaqui\'e, log schemes after Kato and congruence schemes after
Berkovich and Deitmar.

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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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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: acc-phys
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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: chao-dyn
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The categories of this paper are: bayes-an