Automorphisms of curves and the lifting conjecture

[摘要] It is an open question whether or not one can always lift Galois extensions of smoothalgebraic curves in characteristic p to Galois extensions of smooth relative curves in characteristic0. In this thesis we study some of the available techniques and partial solutionsto this problem.Our studies include the techniques of Oort, Sekiguchi and Suwa where the lifting problemis approached via a connection with lifting group schemes. We then move to the topic ofsingular liftings and for this we study the approach of Garuti. Thereafter, we move to thewild smooth setting again where we study the crucial local − global principle, and applyit by illustrating how Green and Matignon solved the p2-lifting problem.

[发布机构] Stellenbosch University