Local Fields and Their Extensions

This text is devoted to the study of complete discrete valuation fields with perfect residue fields. One special feature is the absence of cohomology; although most specialists would find it difficult to conceive of serious discussions in this area without the application of cohomology groups, the authors believe that many problems can be presented more rationally when based on more natural, explicit constructions. In addition, a cohomology-free treatment seems to be preferable for those who are encountering this subject for the first time. The main prerequisite is a standard graduate course in algebra, and familiarity with *r-adic fields is also helpful background.