Sections over Finite Fields

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


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.


Finite Field Elliptic Curf Abelian Variety Projective Curve Absolute Galois Group 
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  1. LMD90.
    Lachaud, G., Martin-Deschamps, M.: Nombre de points des jacobiennes sur un corps fini. Acta Arithmetica 56, 329–340 (1990)MathSciNetzbMATHGoogle Scholar
  2. McR71.
    MacRae, R.E.: On unique factorization in certain rings of algebraic functions. J. Algebra 17, 243–261 (1971)MathSciNetzbMATHCrossRefGoogle Scholar
  3. S+08.
    Stein, W.A., et al.: Sage Mathematics Software (Version 3.1.4), The Sage Development Team. (2008)
  4. Ta97.
    Tamagawa, A.: The Grothendieck conjecture for affine curves. Compos. Math. 109(2), 135–194 (1997)MathSciNetzbMATHCrossRefGoogle 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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