$p$-Adic Integral Geometry
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.
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Information & Authors
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Published In
SIAM Journal on Applied Algebra and Geometry
Pages: 28 - 59
DOI: 10.1137/19M1284737
ISSN (online): 2470-6566
Copyright
© 2021, Society for Industrial and Applied Mathematics.
History
Submitted: 3 September 2019
Accepted: 6 October 2020
Published online: 4 January 2021
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