Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the multiplicities of a motive   We study the multiplicities of pure motives modulo numerical equivalence,
which are defined as scalars comparing the tannakian trace with the
ring-theoretic trace. Our general set-up is that of a rigid semi-simple tensor
category such that End(1) is a field of characteristic 0. The main result is
that, due to the existence of a Weil cohomology theory (to be defined
appropriately in the general set-up), the multiplicities are integers. This
property is sufficient for the rationality (and functional equation) of the
zeta function of an (invertible) endomorphism. We also show that the classical
equivalent conditions to the Tate conjecture for pure motives over a finite
field are of category-theoretic nature in the sense that they can be proven in
the above abstract set-up.

21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an