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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Lachaud, G., Martin-Deschamps, M.: Nombre de points des jacobiennes sur un corps fini. Acta Arithmetica 56, 329–340 (1990)
MacRae, R.E.: On unique factorization in certain rings of algebraic functions. J. Algebra 17, 243–261 (1971)
Stein, W.A., et al.: Sage Mathematics Software (Version 3.1.4), The Sage Development Team. http://www.sagemath.org http://www.sagemath.org (2008)
Tamagawa, A.: The Grothendieck conjecture for affine curves. Compos. Math. 109(2), 135–194 (1997)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Stix, J. (2013). Sections over Finite Fields. In: Rational Points and Arithmetic of Fundamental Groups. Lecture Notes in Mathematics, vol 2054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30674-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-30674-7_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30673-0
Online ISBN: 978-3-642-30674-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
