Non-Archimedean and motivic stationary phase formulas
T\'eofil Adamski
TL;DR
This paper revisits stationary phase formulas for non-degenerate singular phases over non-Archimedean fields and introduces a motivic analogue using advanced motivic integration techniques.
Contribution
It provides a new motivic version of Heifetz's stationary phase formula in the non-Archimedean setting, expanding the theoretical framework.
Findings
Reconsideration of Heifetz's stationary phase formula for non-degenerate singular phases
Development of a motivic analogue using Cluckers-Loeser's motivic integration
Extension of stationary phase analysis to a motivic context
Abstract
In this article, for a non degenerate singular phase, we reconsider a stationary phase formula of Heifetz in the non-Archimedean local field setting and give a motivic analogue using Cluckers-Loeser's motivic integration.
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