Member 9: University of Nottingham,
School of Mathematical Sciences
Team Members
John Cremona,
Ivan Fesenko, Michael Spiess, John Coates (Cambridge), Victor Flynn (Liverpool)
Dr. Susan Howson, M. Taylor (Manchester)
Main Research Themes
Studying properties of the nonabelian reciprocity cocycle
(recently defined by Fesenko) for arithmetically profinite Galois
extensions of local fields: the image, functorial properties, links to
local Langlands, Galois cohomologies, Galois representations, local
inverse Galois theory and ramification theory. To extend this theory
to higher dimensional local fields.
Arithmetic of curves of genus 1 and 2 over number fields,
especially algorithmic aspects, explicit investigations and
descriptions of Shafarevich-Tate groups and Birch-Swinnerton-Dyer
conjecture over number fields, links with modular curves,
higher-dimensional Birch-SD conjectures, covering collections of
curves. Theoretical and numerical attack on these problems by the
methods of Iwasawa Theory.
Tamely ramified higher dimensional class field theory of
arithmetic schemes: to consider regular schemes of finite type over
Spec(Z) which are not necessarily proper; to describe the tamely
ramified coverings (with respect to a completion $X -> \bar{X})$ in
terms of the Suslin homology of $X$.