Submission date: 3 March 2020

Abstract:

We prove that if two semi-algebraic subsets of ℚ_p^n have the same p-adic measure, then this equality can already be deduced using only some basic integral transformation rules. On the one hand, this can be considered as a positive answer to a p-adic analogue of a question asked by Kontsevich-Zagier in the reals (though the question in the reals is much harder). On the other hand, our result can also be considered as stating that over ℚp, universal motivic integration (in the sense of Hrushovski-Kazhdan) is just p-adic integration.

Mathematics Subject Classification: 11S80 (Primary) 03C10, 03C60, 03C65, 03C98, 12L12, 14E18, 14G20 (Secondary)

Keywords and phrases:

Full text arXiv 2003.01500: pdf, ps.