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Recovering function fields from their decomposition graphs

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Number Theory, Analysis and Geometry

Abstract

We develop the global theory of a strategy to tackle a program initiated by Bogomolov in 1990. That program aims at giving a group-theoretical recipe by which one can reconstruct function fields K | k with td(K | k) > 1 and k algebraically closed from the maximal pro-ℓ abelian-by-central Galois group Π K c of K, where ℓ is any prime number ≠char(k).

Mathematics Subject Classification (2010): Primary 12E, 14E, 14H, 14J Secondary 12E30, 14E99, 14H30, 14J99

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Notes

  1. 1.

    Recall that for an abelian group A, its ℓ-adic completion is by definition \(\widehat{A} :{=\lim }_{{ \leftarrow\atop e} }\,A/{\mathcal{l}}^{e}\).

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Authors and Affiliations

  1. Dept of Mathematics, University of Pennsylvania, 209 S 33rd St, 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. , Department of Mathematics, Columbia University, Broadway 2990, New York, 10027, New York, USA

    Dorian Goldfeld

  2. , Department of Mathematics, City College of New York, New York, 10031, New York, USA

    Jay Jorgenson

  3. , Department of Mathematics, Yale University, Hillhouse Ave. 10, New Haven, 06520, Connecticut, USA

    Peter Jones

  4. , Department of Mathematics, California Institute of Technology, E. California Blvd. 1200, Pasadena, 91125, California, USA

    Dinakar Ramakrishnan

  5. , Department of Mathematics, University of California at Berkeley, Evans Hall 925, Berkeley, 94720-3840, California, USA

    Kenneth Ribet

  6. , Department of Mathematics, Harvard University, Science Center/One Oxford Street, Cambridge, 02138, Massachusetts, USA

    John Tate

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In memory of Serge Lang

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Pop, F. (2012). Recovering function fields from their decomposition graphs. In: Goldfeld, D., Jorgenson, J., Jones, P., Ramakrishnan, D., Ribet, K., Tate, J. (eds) Number Theory, Analysis and Geometry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1260-1_24

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