Microlocal geometry and valued fields
The article is an overview of some recent connections between non-archimedean geometry and microlocal analysis, with some emphasis on the motivic Milnor fiber and the properties of tangent cones. In both cases the discussions start with the \(p\)-adic version which provides a useful model before setting the motivic picture. The first specific topic includes the following: the motivic zeta function, the motivic Milnor fiber, convolution and Thom-Sebastiani type results (of Denef-Loeser and Looijenga), questions and speculations involving composed maps of type \(P(f,g)\), the analogues of the Steenbrink conjecture about series (result of Guibert-Loeser-Merle), and connections with the Kontsevich-Soibelman conjecture. The second part reviews some results of Cluckers, Comte and Loeser.
scientific article; zbMATH DE number 5931053