p-adic Integral Geometry

Avinash Kulkarni and Antonio Lerario

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Submission date: 03. Sep. 2019
Pages: 27
Bibtex
MSC-Numbers: 53C65, 11S80
Keywords and phrases: Integral Geometry Formula, p-adic volume, zeros of random polynomials.
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Abstract:
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 p^m reduction of a projective set (reproving a result by Oesterlé) and to the study of random p-adic polynomial systems of equations.