Extension of Galois Groups by Solvable Groups, and Application to Fundamental Groups of Curves

  • Niels BorneEmail author
Conference paper
Part of the Progress in Mathematics book series (PM, volume 304)


The issue of extending a given Galois group is conveniently expressed in terms of embedding problems. If the kernel is an abelian group, a natural method, due to Serre, reduces the problem to the computation of an étale cohomology group, that can in turn be carried out thanks to Grothendieck-Ogg-Shafarevich formula. After introducing these tools, we give two applications to fundamental groups of curves.


Fundamental groups of curves embedding problems Grothendieck-Ogg-Shafarevich formula 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Cité scientifique U.M.R. CNRS 8524, U.F.R. de MathématiquesUniversité Lille 1Villeneuve d’Ascq CédexFrance

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