| Résume | Joint Work with Michele Serra. In his paper " Automorphisms of fields of formal power series" (Bull. Am. Math. Soc. 50, 1944) Otto Schilling described the automorphism group of k((t)), the field of Laurent series with coefficients in a ground field k and exponents in the group of integers. In our paper "The automorphism group of a valued field of generalised formal power series" (J. Algebra 605, 2022) we generalise his results to the field k((G)), where G in an arbitrary ordered abelian group. We describe the automorphism group of k((G)) in terms of those of its residue field k, its value group G, and the group of 1- units of its valuation ring.
In particular, we analyse the subgroup of strongly linear automorphisms, that is, automorphisms which commute with infinite sums.
Our results also apply to the field of surreal numbers, as well as to a large class of distinguished subfields of k((G)).
We will therefore discuss necessary and sufficient conditions on a valued field (K,v) (with residue field k and value group G), so that it admits a "distinguished Kaplansky-embedding" into k((G)).
The talk will be self contained talk and geared towards a general audience. |
