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( AEnglischA )

We define an overconvergent version of the Hyodo–Kato complex for semi-stable varieties Y over perfect fields of positive characteristic, and prove that its hypercohomology tensored with Q recovers the log-rigid cohomology when Y is quasi-projective. We then describe the monodromy operator using the overconvergent Hyodo–Kato complex. Finally, we show that overconvergent Hyodo–Kato cohomology agrees with log-crystalline cohomology in the projective semi-stable case.