On a comparison of Gauss sums with products of Lagrange resolvents
On a conjecture concerning minus parts in the style of Gross
On Chinburg's second conjecture for abelian fields.
On equivariant Dedekind zeta-functions at .
On finite linear groups stable under Galois operation.
On Galois structure of the integers in cyclic extensions of local number fields
Let be a rational prime, be a finite extension of the field of -adic numbers, and let be a totally ramified cyclic extension of degree . Restrict the first ramification number of to about half of its possible values, where denotes the absolute ramification index of . Under this loose condition, we explicitly determine the -module structure of the ring of integers of , where denotes the -adic integers and denotes the Galois group Gal. In the process of determining this structure,...
On Hilbert-Speiser type imaginary quadratic fields
On integral normal bases over intermediary fields
On integral Stark conjectures (and multiplicative Galois module structures).
On normal integral bases in ray class fields over imaginary quadratic fields
On p-adic L-functions and normal bases of rings of integers.
On Rédei's theory of the Pell equation.
On relative integral bases for unramified extensions
0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely generated and...
On Taylor's conjecture for Kummer orders
On the branch order of the ring of integers of an abelian number field
On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field.
On the galois module structure over CM-Fields.
On the Galois structure of algebraic integers and S-units.
On the Galois structure of the square root of the codifferent
Let be a finite abelian extension of , with the ring of algebraic integers of . We investigate the Galois structure of the unique fractional -ideal which (if it exists) is unimodular with respect to the trace form of .
On the infinite fern of Galois representations of unitary type
Let be a CM number field, an odd prime totally split in , and let be the -adic analytic space parameterizing the isomorphism classes of -dimensional semisimple -adic representations of satisfying a selfduality condition “of type ”. We study an analogue of the infinite fern of Gouvêa-Mazur in this context and show that each irreducible component of the Zariski-closure of the modular points in has dimension at least . As important steps, and in any rank, we prove that any first order...