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Franz-Viktor Kuhlmann, Salma Kuhlmann, Murray Marshall - - Preview
|Suppose L = K, with K, a classical p-adic field. Let A C L be a classical locality of |
K . We show that A is p-adically closed and L|A is a finite extension. It is clear that
A is non-real, hence it is p'- adically closed with respect to a finite rational prime ...
|Artin and Schreier's introduction in 1926 of the class of real closed fields, which |
share all the 'algebraic' properties of R. Independently of Ax-Kochen, also Y.
Ershov (see ) introduced the p-adically closed fields in 1965. A more general ...
|p-adic. Fields. In order to be able to define K -valued functions by means of series |
(mainly power series), we have to ... so we shall consider its completion Cp: This
field turns out to be algebraically closed and is a natural domain for the study of ...
|Up to now, we have kept our attention focused on the field Q and its p-adic |
completions. ... Qp in order to obtain a field that is not only complete (so that we
can do analysis) , but also algebraically closed (so that all polynomials have
|We now want to construct a field that contains all zeros of all polynomials over Qp|
. Definition 5.5. Let A' be a ... We are lucky that in the p-adic case by completing
the algebraic closure we again obtain an algebraically closed field. In principle it
|The completion of (Q, | |p) is called the field of p-adic numbers and is denoted by |
(Q, , ). ... A p-adically closed field is a valued field (K, V) such that char(K) = 0, V is
henselian with m(V) = py, k > F, and [F : nP) = n for n = 1,2,3,.... So (Qp, Zp) is a ...
Leonid A. Bokut', Anatoli_ Ivanovich Mal_t_s_ev, Alekse_ Ivanovich Kostrikin - 1992 - Preview - More editions
|Abstract We describe some classes of multiply pseudo-p-adically closed fields, |
admitting only a finite number of p-valuations (but with respect to different primes
p) and having finitely generated absolute Galois groups. These classes have ...
|This monograph is a systematic treatise on period domains over finite and over p-|
adic fields. ... theory quite a bit in some places, especially to accomodate
isocrystals over non-algebraically closed fields, and also isocrystals withG-
|Show that the class of p-adically closed fields is model complete and |
axiomatizable in the language of valued fields. Hints: Apply Theorems 4.1.3 and
4.3.5, and show that the proof of Theorem 4.6.1 carries over to the case of two p-