$p$-adic Integral Geometry

Avinash Kulkarni; Antonio Lerario

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arXiv · 1908.04775

$p$-adic Integral Geometry

Avinash Kulkarni·Antonio Lerario

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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 Oesterl\'e) and to the study of random $p$-adic polynomial systems of equations.

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Avinash Kulkarni, Antonio Lerario. 2019-08-13. $p$-adic Integral Geometry. https://arxiv.org/abs/1908.04775

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