Institution: | Department of Mathematics, University of Stellenbosch, Stellenbosch, 7602, South Africa ; Mathématiques Pures de Bordeaux, UPRS-A 5467, C.N.R.S Université de Bordeaux I, 351, cours de la Libération 33405 -- Talence, Cedex, France |
Abstract: | Let be an algebraically closed field of characteristic the ring of Witt vectors and a complete discrete valuation ring dominating and containing a primitive -th root of unity. Let denote a uniformizing parameter for We study order automorphisms of the formal power series ring which are defined by a series The set of fixed points of is denoted by and we suppose that they are -rational and that for Let be the minimal semi-stable model of the -adic open disc over in which specializes to distinct smooth points. We study the differential data that can be associated to each irreducible component of the special fibre of Using this data we show that if , then the fixed points are equidistant, and that there are only a finite number of conjugacy classes of order automorphisms in which are not the identity |