For an endomorphism of a p-adic variety that extends to an integral model, every integral periodic point has primitive period at most the special fiber size times a p-power factor times (|k|^{d'} - 1), with d' the maximum cotangent dimension in the special fiber.
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Uniform Bounds for Periods of Endomorphisms of Varieties
For an endomorphism of a p-adic variety that extends to an integral model, every integral periodic point has primitive period at most the special fiber size times a p-power factor times (|k|^{d'} - 1), with d' the maximum cotangent dimension in the special fiber.