David Burns

On Galois structure invariants associated to Tate motives

We establish the equivalence of two definitions of invariants measuring the Galois module structure of K-groups of rings of integers in number fields (due to Chinburg et al. on the one hand and the authors on the other). We also make some remarks concerning the possibility of yet another such definition via Lichtenbaum complexes.

Leading terms of Artin L -functions at s =0 and s =1

We formulate an explicit conjecture for the leading term at s = 1 of the equivariant Dedekind zeta-function that is associated to a Galois extension of number fields. We show that this conjecture refines well-known conjectures of Stark and Chinburg, and we use the functional equation of the zeta-function to compare it to a natural conjecture for the leading term at s = 0.

Equivariant Epsilon Constants, Discriminants and Étale Cohomology

Let

On descent theory and main conjectures in non-commutative Iwasawa theory

L/K

L-functions and Galois representations

be a finite Galois extension of number fields. We formulate and study a conjectural equality between an element of the relative algebraic K-group

A non-abelian Stickelberger theorem

K_0(\mathbb{Z}[\mathrm{Gal}(L/K)], \mathbb{R})

Equivariant Tamagawa Numbers, Fitting Ideals and Iwasawa Theory

which is constructed from the equivariant Artin epsilon constant of

Grothendieck Groups of Bundles on Varieties over Finite Fields

L/K

Annihilating Selmer modules

and a sum of structural invariants associated to

Explicit units and the equivariant Tamagawa number conjecture, II

L/K