Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded-Tannakian categories of motives   Given a rigid tensor-triangulated category and a vector space valued
homological functor for which the K\"{u}nneth isomorphism holds, we construct a
universal graded-Tannakian category through which the given homological functor
factors. We use this to (unconditionally) construct graded-Tannakian categories
of pure motives associated to a fixed Weil cohomology theory, with a fiber
functor realizing the given cohomology theory. For $\ell$-adic cohomology and a
ground field which is algebraic over a finite field, this category is
Tannakian. In this case, we obtain in particular motivic Galois groups which
act naturally on $\ell$-adic cohomology without assuming any of the standard
conjectures. We show that these graded-Tannakian categories are equivalent to
Grothendieck's category of pure motives if the standard conjecture D holds.

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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph