Glasgow Mathematical Journal

Table of Contents - September 2012 - Volume 54, Issue 03  

Research Article

AN ALGEBRAIC-METRIC EQUIVALENCE RELATION OVER p-ADIC FIELDS

MARIAN VÂJÂITUa1 and ALEXANDRU ZAHARESCUa2

a1 Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P. O. Box 1-764, RO-014700 Bucharest, Romania e-mail: Marian.Vajaitu@imar.ro

a2 Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA e-mail: zaharesc@math.uiuc.edu

Abstract

Let p be a prime number, Q p the field of p-adic numbers, K a finite field extension of Q p , K a fixed algebraic closure of K and C p the completion of K with respect to the p-adic valuation. We introduce and investigate an equivalence relation on C p , defined in terms of field extensions and metric properties of Galois orbits over K.

(Received November 24 2011)

(Revised March 13 2012)

(Accepted April 17 2012)

2000 Mathematics Subject Classification

  • 11S99