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arXiv · 2103.01811

Motivic integration on Berkovich spaces

Tommaso de Fernex·Chung Ching Lau
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Abstract

We define a motivic measure on the Berkovich analytification of an algebraic variety defined over a trivially valued field, and introduce motivic integration in this setting. The construction is geometric with a similar spirit as Kontsevich's original definition, and leads to the formulation of a functorial theory which mirrors, in this aspect, the approach of Cluckers and Loeser via constructibe motivic functions. A version of the integral over nontrivially valued fields and its relation to Hrushovski and Kazhdan's integration are also discussed.

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Tommaso de Fernex, Chung Ching Lau. 2021-03-02. Motivic integration on Berkovich spaces. https://arxiv.org/abs/2103.01811

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