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The $\mathbb{Z}/p$ metabelian birational $p$-adic section conjecture for varieties

Part of: General field theory

Published online by Cambridge University Press:  04 May 2017

Florian Pop
Florian Pop*
Affiliation:
Department of Mathematics, University of Pennsylvania, DRL, 209 S 33rd Street, Philadelphia, PA 19104, USA email pop@math.upenn.edu
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Abstract

We generalize the $\mathbb{Z}/p$metabelian birational $p$-adic section conjecture for curves, as introduced and proved in Pop [On the birational$p$-adic section conjecture, Compos. Math. 146 (2010), 621–637], to all complete smooth varieties, provided $p>2$. The condition $p>2$ seems to be of technical nature only, and might be removable.

Keywords

anabelian geometryabsolute Galois groupsmetabelian Galois groupsp-adically closed fieldsrational pointsvaluationsHilbert decomposition theory(birational) section conjecture

MSC classification

Secondary: 12E30: Field arithmetic
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 7 , July 2017 , pp. 1433 - 1445
Copyright
© The Author 2017 

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