Sections over Finite Fields

  • Jakob Stix
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2054)

Abstract

Let \({\mathbb{F}}_{q}\) be a finite field with q elements of characteristic p. The absolute Galois group \({\mathrm{Gal}}_{{\mathbb{F}}_{q}}\) is profinite free and generated by the qth-power Frobenius \({Frob }_{q}\). Thus any extension of \({\mathrm{Gal}}_{{\mathbb{F}}_{q}}\) splits, and does so most likely in an abundant number of inequivalent ways.

Keywords

Finite Field Elliptic Curf Abelian Variety Projective Curve Absolute Galois Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    Tamagawa, A.: The Grothendieck conjecture for affine curves. Compos. Math. 109(2), 135–194 (1997)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jakob Stix
    • 1
  1. 1.Mathematics Center Heidelberg (MATCH)University of HeidelbergHeidelbergGermany

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