Extensions of discrete valuations and their ramification theory

Official URL: http://192.168.1.20/record=b1378279 (Table of Contents)

We study how a discrete valuation v on a field K can be extended to a valuation of a finite separable extension L of K. The ramification theory of extensions of discrete valuations to a finite separable extension is very well established whenever the residue class field extension is separable. This is the so called classical ramification theory. We investigate the classical ramification theory and also the ramification theory of extensions of discrete valuations with an inseparable residue class field extension. We show that some results from classical ramification theory, such as Hilbert's different formula can be modified to be true for extensions of valuations with inseparable residue class field extensions, whereas many other classical results fail to hold.