p进积分几何

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Applied Algebra and Geometry Pub Date : 2019-08-13 DOI:10.1137/19m1284737

Avinash Kulkarni, A. Lerário

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引用次数: 16

摘要

证明了两个$p$进射影代数集的交点求平均值的$p$进积分几何公式的一个$p$进版本。我们应用这一结果给出了投影集的模p^m约简中的点个数的界(对Oesterl\'e的一个结果进行了改进)，并应用于随机p$-进多项式方程组的研究。

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p-Adic Integral Geometry

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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