Microlocal geometry and valued fields
type: Item
instance of: scholarly article
title: Microlocal geometry and valued fields
zbMATH Open document ID: 1238.11070
DOI: 10.2977/PRIMS/46
author: François Loeser
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2011-07-22T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11G25
Mathematics Subject Classification ID: 03C65
Mathematics Subject Classification ID: 03C98
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14G27
zbMATH DE Number: 5931053
zbMATH Keywords: non-archimedean geometry
zbMATH Keywords: valued fields
zbMATH Keywords: Milnor fiber
zbMATH Keywords: tangent cones
zbMATH Keywords: microlocal geometry
reviewed by: András Némethi
MaRDI profile type: Publication
cites work: Microlocal \(\ell \)-adic analysis in characteristic \(p>0\) in the case of a trait
cites work: Asymptotic curve of fibre- integrals
cites work: Motivic degree zero Donaldson-Thomas invariants
cites work: On motivic zeta functions and the motivic nearby fiber
full work available at URL: https://doi.org/10.2977/prims/46
OpenAlex ID: W2082223009
description: scientific article; zbMATH DE number 5931053