Steinitz classes of tamely ramified Galois extensions of algebraic number fields
Speaker: Dr. Alessandro Cobbe (Scuola Normale Superiore, Pisa)
Date: Wed 17th February 2010
Location: Mathematical Sciences Seminar Room
The Steinitz class of a number field extension L/K is an ideal class in the ring of integers O_K of K, which, together with the degree [L:K] of the extension, determines the O_K-module structure of O_L. The set of all the realizable Steinitz classes for a number field K and a finite group G is denoted by R_t(K,G). For some groups, such as abelian groups, it is known that this set is a subgroup of the ideal class group of K; it is conjectured that this is true for all groups of finite order. In my talk I will describe some nonabelian groups for which the conjecture can be proved using techniques from class field theory, and I will give some ideas about how these results can be obtained.
(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)