### arXiv:1908.04775 [math.AG]AbstractReferencesReviewsResources

#### $p$-adic Integral Geometry

Avinash Kulkarni, Antonio Lerario

Published 2019-08-13Version 1

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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