p-adic Integral Geometry
Avinash Kulkarni and Antonio Lerario
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Submission date: 03. Sep. 2019
MSC-Numbers: 53C65, 11S80
Keywords and phrases: Integral Geometry Formula, p-adic volume, zeros of random polynomials.
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Link to arXiv: See the arXiv entry of this preprint.
We prove a p-adic version of the Integral Geometry Formula for averaging the intersection of two p-adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo pm reduction of a projective set (reproving a result by Oesterlé) and to the study of random p-adic polynomial systems of equations.