Algebraic valuation ring extensions as limits of complete intersection algebras

Algebraic Extensions of Normed Algebras

Disclaimer: This dissertation does not contain plagiarised material; except where otherwise stated all theorems are the author's. Acknowledgement: Many thanks to Joel Feinstein for guidance with the literature, useful suggestions and comments on this work.

Algebraic Extensions of Continuous Function Algebras

Ring graphs and complete intersection toric ideals

We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs correspond to ring graphs and that these ideal...

Explicit abelian extensions of complete discrete valuation fields

For higher class field theory Witt and Kummer extensions are very important. In fact, Parshin’s construction of class field theory for higher local fields of prime characteristic [P] is based on an explicit (Artin–Schreier–Witt) pairing; see [F] for a generalization to the case of a perfect residue field. Kummer extensions in the mixed characteristic case can be described by using class field t...

Realizability of Algebraic Galois Extensions by Strictly Commutative Ring Spectra

We discuss some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict attention to the case of finite Galois groups and to global Galois extensions. We describe parts of the general framework developed by Rognes. Central rôles are played by the notion of strong duality and a trace mapping constructed by Greenlees and May in the context ...