nt.number theory - References for Artin motives

A motive is a chunk of a variety cut out by correspondences. (If you like, it is something of which we can take cohomology.)

Artin motives are what one gets by restricting to zero-dimensional varieties. If the ground
field is algebraically closed then zero-dimensional varieties are simply finite unions of points, so there is not much to say; the only invariant is the number of points.

But if the ground field $K$ is not algebraically closed (but is perfect, e.g. char $0$,
so that we can describe all finite extensions by Galois theory), then there are many
interesting $0$-dimensional motives, and in fact the category of Artin motives (with
coefficients in a field $F$ of characteristic $0$, say) is equal to the category of continuous
representations of $Gal(overline{K}/K)$ on $F$-vector spaces (where the $F$-vector spaces are given their discrete topoogy; in other words, the representation must factor through $Gal(E/K)$ for some finite extension $E$ of $K$).

Perhaps from a geometric perspective, these motives seem less interesting than others. On the other hand, number theoretically, they are very challenging to understand. The Artin conjecture about the holomorphicity of $L$-functions of Artin motives, which is the basic reciprocity conjecture regarding such motives, remains very wide open, with very few non-abelian cases known. (Of course, for representations with abelian image, these
conjectures amount to class field theory, which is already quite non-trivial.)

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