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WAVE FRONT HOLONOMICITY OF Cexp-CLASS DISTRIBUTIONS ON NON-ARCHIMEDEAN LOCAL FIELDS.
- Source :
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Forum of Mathematics, Sigma . 2020, Vol. 8, p1-35. 35p. - Publication Year :
- 2020
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Abstract
- Many phenomena in geometry and analysis can be explained via the theory of D-modules, but this theory explains close to nothing in the non-archimedean case, by the absence of integration by parts. Hence there is a need to look for alternatives. A central example of a notion based on the theory of D-modules is the notion of holonomic distributions. We study two recent alternatives of this notion in the context of distributions on non-archimedean local fields, namely Cexp-class distributions from Cluckers et al. ['Distributions and wave front sets in the uniform nonarchimedean setting', Trans. Lond. Math. Soc.5(1) (2018), 97–131] and WF-holonomicity from Aizenbud and Drinfeld ['The wave front set of the Fourier transform of algebraic measures', Israel J. Math.207(2) (2015), 527–580 (English)]. We answer a question from Aizenbud and Drinfeld ['The wave front set of the Fourier transform of algebraic measures', Israel J. Math.207(2) (2015), 527–580 (English)] by showing that each distribution of the Cexp-class is WF-holonomic and thus provides a framework of WF-holonomic distributions, which is stable under taking Fourier transforms. This is interesting because the Cexp-class contains many natural distributions, in particular, the distributions studied by Aizenbud and Drinfeld ['The wave front set of the Fourier transform of algebraic measures', Israel J. Math.207(2) (2015), 527–580 (English)]. We show also another stability result of this class, namely, one can regularize distributions without leaving the Cexp-class. We strengthen a link from Cluckers et al. ['Distributions and wave front sets in the uniform nonarchimedean setting', Trans. Lond. Math. Soc.5(1) (2018), 97–131] between zero loci and smooth loci for functions and distributions of the Cexp-class. A key ingredient is a new resolution result for subanalytic functions (by alterations), based on embedded resolution for analytic functions and model theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20505094
- Volume :
- 8
- Database :
- Academic Search Index
- Journal :
- Forum of Mathematics, Sigma
- Publication Type :
- Academic Journal
- Accession number :
- 146083884
- Full Text :
- https://doi.org/10.1017/fms.2020.27