p-adic Integral Geometry

2019/08/13 by Kulkarni, Avinash, Lerario, Antonio
#Algebraic Geometry (math.AG) #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.1908.04775

Abstract

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 Oesterlé) and to the study of random p-adic polynomial systems of equations.

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