$p$-adic Integral Geometry
Algebraic Geometry
2019-08-14 v1 Metric Geometry
Number Theory
Probability
Abstract
We prove a -adic version of the Integral Geometry Formula for averaging the intersection of two -adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo reduction of a projective set (reproving a result by Oesterl\'e) and to the study of random -adic polynomial systems of equations.
Cite
@article{arxiv.1908.04775,
title = {$p$-adic Integral Geometry},
author = {Avinash Kulkarni and Antonio Lerario},
journal= {arXiv preprint arXiv:1908.04775},
year = {2019}
}