\(p\)-adic integral geometry. (English) Zbl 1457.53054
Summary: 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.
MSC:
| 53C65 | Integral geometry |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
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