Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The combinatorial-motivic nature of $\mathbb{F}_1$-schemes   We review Deitmar's theory of monoidal schemes to start with, and have a
detailed look at the standard examples. It is explained how one can
combinatorially study such schemes through a generalization of graph theory. In
a more general setting we then introduce the author's version of
$\mathbb{F}_1$-schemes (called $\Upsilon$-schemes here), after which we study
Grothendieck's motives in some detail in order to pass to "absolute motives".
Throughout several considerations about absolute zeta functions are written. In
a final part of the chapter, we describe the approach of Connes and Consani to
understand the ad`ele class space through hyperring extension theory, in which
a marvelous connection is revealed with certain group actions on projective
spaces, and brand new results in the latter context are described. Many
questions are posed, conjectures are stated and speculations are made.

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga