Thesis (MSc (Mathematics))--University of Stellenboswch, 2010. / ENGLISH ABSTRACT: In the work of Green and Matignon it was shown that the Oort-Sekiguchi
conjecture is equivalent to a local question of lifting automorphisms of power
series rings. The Oort-Sekiguchi conjecture asks when an algebraic curve
in characteristic p can be lifted to a relative curve in characteristic 0, while
keeping the same automorphism group. The local formulation asks when an
automorphism of a power series ring over a field k of characteristic p can be
lifted to an automorphism of a power series ring over a discrete valuation
ring with residue field k of the same order as the original automorphism.
This thesis looks at the local formulation and surveys many of the results
for this case. At the end it presents a new theorem giving a Hensel's Lemma
type sufficient condition under which lifting is possible. / AFRIKAANSE OPSOMMING: Green en Matignon het bewys dat die Oort-Sekiguchi vermoede ekwivalent
is aan `n lokale vraag oor of outomorfismes van magsreeksringe gelig kan
word. Die Oort-Sekiguchi vermoede vra of `n algebra ese kromme in karakteristiek
p gelig kan word na `n relatiewe kromme in karakteristiek 0, terwyl
dit dieselfde outomorfisme groep behou. Die lokale vraag vra wanneer
`n outomorfisme van `n magsreeksring oor `n liggaam k van karakteristiek
p gelig kan word na `n outomorfisme van `n magsreeksring oor `n diskrete
waarderingsring met residuliggaam k, terwyl dit dieselfde orde behou as die
aanvanklike outomorfisme.
Hierdie tesis fokus op die lokale vraag en bied `n opsomming van baie
bekende resultate vir hierdie geval. Aan die einde word `n nuwe stelling
aangebied wat voorwaardes stel waaronder hierdie vraag positief beantwoord
kan word.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/5243 |
| Date | 12 1900 |
| Creators | Basson, Dirk (Dirk Johannes) |
| Contributors | Green, B. W., University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 57 p. |
| Rights | University of Stellenbosch |
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