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AN ALGEBRAIC-METRIC EQUIVALENCE RELATION OVER p-ADIC FIELDS

Published online by Cambridge University Press:  31 July 2012

MARIAN VÂJÂITU  and
ALEXANDRU ZAHARESCU
MARIAN VÂJÂITU
Affiliation:
Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P. O. Box 1-764, RO-014700 Bucharest, Romania e-mail: [email protected]
ALEXANDRU ZAHARESCU
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA e-mail: [email protected]
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Abstract

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

Keywords

11S99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 715 - 720
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Alexandru, V., Popescu, N. and Zaharescu, A., On the closed subfields of Cp, J. Number Theory 68 (2)(1998), 131–150.CrossRefGoogle Scholar
2.Alexandru, V., Popescu, N. and Zaharescu, A., The generating degree of Cp, Canad. Math. Bull. 44 (1) (2001), 3–11.Google Scholar
3.Alexandru, V., Popescu, N. and Zaharescu, A., Trace on Cp, J. Number Theory 88 (1) (2001), 13–48.CrossRefGoogle Scholar
4.Ax, J., Zeros of polynomials over local fields – The Galois action, J. Algebra 15 (1970), 417–428.CrossRefGoogle Scholar
5.Barsky, D., Transformation de Cauchy p-adique et algèbre d'Iwasawa, Math. Ann. 232 (3) (1978), 255–266.CrossRefGoogle Scholar
6.Ioviţă, A. and Zaharescu, A., Completions of r.a.t.-valued fields of rational functions, J. Number Theory 50 (2) (1995), 202–205.CrossRefGoogle Scholar
7.Mazur, B. and Swinnerton-Dyer, P., Arithmetic of Weil curves, Invent. Math. 25 (1974), 1–61.Google Scholar
8.Sen, S., On automorphisms of local fields, Ann. Math. 90 (2) (1969), 33–46.CrossRefGoogle Scholar
9.Tate, J. T., p-divisible groups, in Proc. Conf. Local Fields, Driebergen, 1966 (Springer, Berlin, Germany, 1967) 158–183.CrossRefGoogle Scholar
10.Zaharescu, A., A metric symbol for pairs of polynomials over local fields, C.R. Math. Acad. Sci. Soc. R. Can. 22 (4) (2000), 147–150.Google Scholar
11.Zaharescu, A., Lipschitzian elements over p-adic fields, Glasgow Math. J. 47 (2005), 363–372.Google Scholar