| Résume | Recall that a field K is large if it is existentially closed in K((t)). Examples of such fields are the complex, the real, and the p-adic numbers. This class of fields has been exploited significantly by F. Pop and others in inverse Galois-theoretic problems. In recent work with M. Tressl we introduced and explored a differential analogue of largeness, that we conveniently call “differentially large”. I will present some properties of such fields, and use a twisted version of the Taylor morphism to characterise them using formal Laurent series and to even construct “natural” examples (which ultimately yield examples of DCFs and CODFs... acronyms that will be explained in the talk). |
