Extension of Galois Groups by Solvable Groups, and Application to Fundamental Groups of Curves
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.
KeywordsFundamental groups of curves embedding problems Grothendieck-Ogg-Shafarevich formula
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