TITLE: References for Artin motives
QUESTION [17 upvotes]: I find the following description of Artin motives in Wikipedia. Since these seem to be quite related to number theory, I am interested to learn more in that context. I request the experts available in MO to provide me a reference which can be more useful to me than this terse description. Any comments and explanations also will be helpful. I apologize for asking a seemingly basic question; but I find it impossible to wade through the numerous references available on motives.
Fix a field $k$ and consider the functor
finite separable extensions $K$ of $k$ → finite sets with a (continuous) action of the absolute Galois group of $k$
which maps $K$ to the (finite) set of embeddings of $K$ into an algebraic closure of $k$. In Galois theory this functor is shown to be an equivalence of categories. Notice that fields are $0$-dimensional. Motives of this kind are called Artin motives. By $\mathbb Q$-linearizing the above objects, another way of expressing the above is to say that Artin motives are equivalent to finite $\mathbb Q$-vector spaces together with an action of the Galois group.
I have some idea of what are pure motives and mixed motives, in the context of algebraic varieties. What I exactly have in mind is to understand the modern statement of equivariant Tamagawa number conjecture. This would appear to be the simplest instance to keep in mind, if I go ahead.

REPLY [16 votes]: 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.)