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On the birational p-adic section conjecture

Part of: General field theory

Published online by Cambridge University Press:  18 March 2010

Florian Pop
Florian Pop*
Affiliation:
Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA (email: [email protected])
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Abstract

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In this article we introduce and prove a ℤ/p meta-abelian form of the birationalp-adic section conjecture for curves. This is a much stronger result than the usual p-adic birational section conjecture for curves, and makes an effective p-adic section conjecture for curves quite plausible.

Keywords

anabelian geometry(étale) fundamental groupsp-adically closed fieldslocal–global principles for Brauer groupsrational pointsvaluationsHilbert decomposition theory

MSC classification

Secondary: 12E30: Field arithmetic
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 3 , May 2010 , pp. 621 - 637
Copyright
Copyright © Foundation Compositio Mathematica 2010

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