On Weil-etale cohomology and Artin L-series

We prove a K-theoretical leading term formula relating the Artin L-series that<br/>arise from a finite Galois covering of separated schemes over a finite field to an equivariant Euler characteristic of the compactly supported Weil-etale cohomology of Z. We deduce from this result an explicit characterization of the Galois structure of the compactly supported Weil-etale cohomology complex of Z and also the proof for global function fields of a range of previously formulated conjectures including the Ω(3)-Conjecture of Chinburg, the non-abelian Brumer-Stark Conjecture of Nickel and the analogue for function fields of the equivariant Tamagawa number conjecture for untwisted Tate motives. As a key step in the proof of our main result we establish several new results concerning the K-theory<br/>of group rings over Tate algebras that are of independent interest.