Constructing complete distinguished chains with given invariants.

Let v be a henselian valuation of arbitrary rank of a field K with value group G(K) and residue field R(K) and be the unique extension of v to a fixed algebraic closure of K with value group . It is known that a complete distinguished chain for an element θ belonging to with respect to (K, v) gives rise to several invariants associated to θ, including a chain of subgroups of , a tower of fields, together with a sequence of elements belonging to which are the same for all K-conjugates of θ. These invariants satisfy some fundamental relations. In this paper, we deal with the converse: Given a chain of subgroups of containing G(K), a tower of extension fields of R(K), and a finite sequence of elements of satisfying certain properties, it is shown that there exists a complete distinguished chain for an element associated to these invariants. We use the notion of lifting of polynomials to construct it. [ABSTRACT FROM AUTHOR]