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Journals and Conferences
We define motivic Artin L-functions and show that they specialize to the usual Artin L-functions under the trace of Frobenius. In the last section we use our L-functions to prove a motivic analogue of the Chebotarev density theorem.
For fields F of characteristic not p containing a primitive pth root of unity, we determine the Galois module structure of the group of pth-power classes of K for all cyclic extensions K/F of degree p. The foundation of the study of the maximal p-extensions of fields K containing a primitive pth root of unity is a group of the pth-power classes of the… (More)
In the mid-1960s Borevič and Faddeev initiated the study of the Galois module structure of groups of pth-power classes of cyclic extensions K/F of pth-power degree. They determined the structure of these modules in the case when F is a local field. In this paper we determine these Galois modules for all base fields F .
Let p be a prime, F a field containing a primitive pth root of unity, and E/F a cyclic extension of degree p. Using the Bloch–Kato Conjecture we determine precise conditions for the cohomology group Hn(E) := H(GE ,Fp) to be free or trivial as an Fp[Gal(E/F )]-module, and we examine when these properties for Hn(E) are inherited by Hk(E), k > n. By analogy… (More)
Let K be a cyclic Galois extension of degree p over a field F containing a primitive pth root of unity. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F ) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F )]modules. For these embedding problems we prove conditions on solvability, formulas for… (More)
One of the fundamental questions in current field theory, related to Grothendieck’s conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the fields themselves. In this paper we initiate the classification of additive properties of multiplicative subgroups of… (More)
We study quadratic forms that can occur as trace forms qL/K of Galois field extensions L/K, under the assumption that K contains a primitive 4th root of unity. M. Epkenhans conjectured that qL/K is always a scaled Pfister form. We prove this conjecture and classify the finite groups G which admit a G-Galois extension L/K with a nonhyperbolic trace form. We… (More)
Assuming the Bloch-Kato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor ktheory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal p-extension of F is at most n. The key to the Bloch-Kato Conjecture is Hilbert 90 for Milnor Ktheory for… (More)