On the Closed Subfields ofCp

Chains of metric invariants over a local field

“…In this connection we point out that the distinguished sequences (α n ) n∈N associated to T (see [1]) provide in some sense best possible approximations to T , and some of their properties are reminiscent of those of continued fractions associated to real numbers. In particular they have the property that for each such α n the entire chain D K (α n ) (with the obvious exception of…”

“…In many cases one has more information on D K (T ) than on N K (T ) (see for example the constructive approach from [1] and [6] which gives all the elements T of Ω, where the chain D K (T ) is built into the construction). So from this point of view one may interpret Theorem 2 as giving information on the chain N K (T ) in terms of the "known" chain D K (T ).…”

“…These chains D K (α) play an essential role in the description of the structure of irreducible polynomials over K. We mention in this context that they can also be defined in terms of the so-called saturated distinguished chains introduced in [6] and later studied also in [1] and [5]. In this paper we try to keep the presentation short and as self-contained as possible.…”

On the structure of compact subsets of Cp

“…, constructed in [A]. This last basis has deep arithmetical roots (see also [APZ1], [APZ2], [P2]) and it will be studied in another paper.…”

On the closed subfields of Q¯~p${\tilde{\bar Q}}_p$

“…In [1,2] there were proved some results for closed subfields L of C p , namely L D A Q p OEx for certain x 2 L called generic elements. Thus if L=Q p is infinite, L is isomorphic (both algebraically and topologically) to a completion of a polynomial ring Q p OEx with respect to a certain extension to Q p OEx of the p-adic valuation on Q p .…”