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MiS Preprint

$p$-adic Integral Geometry

Avinash Kulkarni and Antonio Lerario


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.

MSC Codes:
53C65, 11S80
Integral Geometry Formula, p-adic volume, zeros of random polynomials.

Related publications

2021 Repository Open Access
Avinash Kulkarni and Antonio Lerario

\(p\)-adic integral geometry

In: SIAM journal on applied algebra and geometry, 5 (2021) 1, pp. 28-59