We prove a $p$-adic version of the integral geometry formula for averaging the intersection of two $p$-adic projective varieties. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective variety (reproving a result by Oesterlé) and to the study of random $p$-adic polynomial systems of equations.
$p$-Adic Integral Geometry / Kulkarni, Avinash; Lerario, Antonio. - In: SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY. - ISSN 2470-6566. - 5:1(2021), pp. 28-59. [10.1137/19M1284737]
$p$-Adic Integral Geometry
Kulkarni, Avinash;Lerario, Antonio
2021-01-01
Abstract
We prove a $p$-adic version of the integral geometry formula for averaging the intersection of two $p$-adic projective varieties. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective variety (reproving a result by Oesterlé) and to the study of random $p$-adic polynomial systems of equations.File in questo prodotto:
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