Abstract:It is a theorem of Kim–Tamagawa that the ‐pro‐unipotent Kummer map associated to a smooth projective curve over a finite extension of is locally constant when . This paper establishes two generalisations of this result. First, we extend the Kim–Tamagawa theorem to the case that is a smooth variety of any dimension. Second, we formulate and prove the analogue of the Kim–Tamagawa theorem in the case , again in arbitrary dimension. In the course of proving the latter, we give a proof of an étale–de Rham compar… Show more
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