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ℤ∕ℓ Abelian-by-Central Galois Theory of Prime Divisors

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Book cover The Arithmetic of Fundamental Groups

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 2))

Abstract

In this manuscript I show how to recover some of the inertia structure of (quasi) divisors of a function field K | k over an algebraically closed base field k from its maximal mod ℓabelian-by-central Galois theory of K, provided td(K | k) > 1. This is a first technical step in trying to extend Bogomolov’s birational anabelian program beyond the full pro-ℓ situation, which corresponds to the limit case modℓ ∞.

Supported by NSF grant DMS-0801144.

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Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, DRL, 209 S 33rd Street, Philadelphia, PA, 19104, USA

    Florian Pop

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  1. Florian Pop
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Correspondence to Florian Pop .

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Editors and Affiliations

  1. MATCH - Mathematics Center Heidelberg, Dept. of Mathematics, Heidelberg University, Im Neuenheimer Feld 288, Heidelberg, 69120, Germany

    Jakob Stix

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Pop, F. (2012). ℤ∕ℓ Abelian-by-Central Galois Theory of Prime Divisors. In: Stix, J. (eds) The Arithmetic of Fundamental Groups. Contributions in Mathematical and Computational Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23905-2_10

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