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There is a notion of $p$-adic period coming from the crystalline Frobeniusautomorphism of the de Rham cohomology of an algebraic variety. In this paper,we consider sequences of $p$-adic periods, one for each prime. We study thesequences using motivic periods, and we formulate an analogue of theGrothendieck period conjecture.

Sequential periods of the crystalline Frobenius