Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On The Motive of G-bundles   Let $G$ be a reductive algebraic group over a perfect field $k$ and $\cG$ a
$G$-bundle over a scheme $X/k$. The main aim of this article is to study the
motive associated with $\cG$, inside the Veovodsky Motivic categories. We
consider the case that $\charakt k=0$ (resp. $\charakt k\geq 0$), the motive
associated to $X$ is geometrically mixed Tate (resp. geometrically cellular)
and $\cG$ is locally trivial for the Zariski (resp. \'etale) topology on $X$
and show that the motive of $\cG$ is geometrically mixed Tate. Moreover for a
general $X$ we construct a nested filtration on the motive associated to $\cG$
in terms of weight polytopes. Along the way we give some applications and
examples.

20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
3
The categories of this paper are: physics