On the structure of Witt -Burnside rings attached to pro-p groups

Abstract

The classical Witt vectors are a ubiquitous object in algebra and number theory. They arise as a functorial construction which takes perfect fields k of characteristic p to p-adically complete discrete valuation rings of characteristic 0 with residue field k and are universal in that sense. Dress and Siebeneicher generalized this construction by producing a functor W_G attached to any profinite group G. The classical case corresponds to the choice G = Z_p. In this thesis we examine the ring structure of some examples of W _G(k) where G is a pro- p group and k is a field of characteristic p. We will show that the structure is surprisingly more complicated than the classical case.