Parametrizing finite order automorphisms of power series rings

[摘要] ENGLISH ABSTRACT: In the work of Green and Matignon it was shown that the Oort-Sekiguchiconjecture is equivalent to a local question of lifting automorphisms of powerseries rings. The Oort-Sekiguchi conjecture asks when an algebraic curvein characteristic p can be lifted to a relative curve in characteristic 0, whilekeeping the same automorphism group. The local formulation asks when anautomorphism of a power series ring over a field k of characteristic p can belifted to an automorphism of a power series ring over a discrete valuationring with residue field k of the same order as the original automorphism.This thesis looks at the local formulation and surveys many of the resultsfor this case. At the end it presents a new theorem giving a Hensel's Lemmatype sufficient condition under which lifting is possible.

[发布机构] Stellenbosch University