Submission date: 2 March 2021

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.

Mathematics Subject Classification: Primary 14E18, Secondary 12J25

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Full text arXiv 2103.01811: pdf, ps.