(References in brackets are to my papers and preprints. Click for more details)
My thesis [1] concerned a refinement by Lichtenbaum of the Stark Conjectures on the leading term at s=0 of Artin L-functions for Galois extensions of number fields. I translated the case of 1-dimensional characters from etale- cohomology into statements on to the Galois structure of class-groups and units which I established for odd Dirichlet characters using Mazur and Wiles' proof of the main Conjecture of Iwasawa Theory over Q.
Subsequent papers [2]-[7] also concern themes in this area, but concentrate on the units and S-units of number fields, either from the constructive viewpoint, or the descriptive one in terms of Galois structure. An example of the latter is [4] which uses Iwasawa theory to study the Galois structure of S-units up to A. Frohlich's relation of canonical factor-equivalence. An example of the constructive approach was the discovery in [5] of `cyclotomic p-units'. These are the analogues for real abelian fields of the classic cyclotomic Gauss sums appearing in Stickelberger's theorem for imaginary abelian fields. They are constructed using a wild variant of the Euler System techniques introduced by Thaine and Kolyvagin. As an application, I gave a weak analogue of Stickelberger's theorem for a real field and conjectured a much stronger version. The Galois structure of cyclotomic p-units was studied in [7]. More recently these elements have appeared in work of J-R. Belliard and T. Nguyen Quang Do and found an application in D. Burns and C. Greither's proof of the equivariant Tamagawa number conjecture for Tate motives over Q. W. Bley has given an analogous construction (with an analogous application to the Tamagawa number conjecture) over an imaginary quadratic field.