Werner Bley

Equivariant Epsilon Constants, Discriminants and Étale Cohomology

Let

Equivariant Tamagawa Numbers, Fitting Ideals and Iwasawa Theory

L/K

Computations in Relative Algebraic K-Groups

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

Numerical Evidence for the Equivariant Birch and Swinnerton-Dyer Conjecture

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

Computation of locally free class groups

which is constructed from the equivariant Artin epsilon constant of

Algorithmic proof of the epsilon constant conjecture

L/K

Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture (Part II)

and a sum of structural invariants associated to

Wild Euler systems of elliptic units and the Equivariant Tamagawa Number Conjecture

L/K

Numerical Evidence for a Conjectural Generalization of Hilbert's Theorem 132

. The precise conjecture is motivated by the requirement that a special case of the equivariant refinement of the Tamagawa Number Conjecture of Bloch and Kato (as formulated by Flach and the second-named author) should be compatible with the functional equation of the associated L-function. We show that, more concretely, our conjecture also suggests a completely systematic refinement of the central approach and results of classical Galois module theory. In particular, the evidence for our conjecture that we present here already strongly refines many of the main results of Galois module theory.

Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions

Let L/K be a finite Galois extension of number fields of group G. In [4] the second named author used complexes arising from étale cohomology of the constant sheaf ℤ to define a canonical element TΩ(L/K) of the relative algebraic K-group K0(ℤ[G],ℝ). It was shown that the Stark and Strong Stark Conjectures for L/K can be reinterpreted in terms of TΩ(L/K), and that the Equivariant Tamagawa Number Conjecture for the ℚ[G]-equivariant motive h0(Spec L) is equivalent to the vanishing of TΩ(L/K). In this paper we give a natural description of TΩ(L/K) in terms of finite G-modules and also, when G is Abelian, in terms of (first) Fitting ideals. By combining this description with techniques of Iwasawa theory we prove that TΩ(L/ℚ) vanishes for an interesting class of Abelian extensions L/ℚ.