Submission date: 13 January 2020

Abstract:

We show that the existential theories of certain algebraic extensions of Q_p are decidable in L_{val}, including Q_p^{ab}, Q_p(p^{1/p^∞}) and Q_p(ζ_{p^∞}). This is done via a local field approximation argument, by passing to the corresponding fields in equicharacteristic p where the answers are known due to Anscombe-Fehm.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2001.04424: pdf, ps.