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From arXiv

Kato complexes of reciprocity sheaves and applications

We show that every reciprocity sheaf gives rise to a cycle (pre)module in the sense of Rost over a perfect field. Over a perfect field of positive characteristic, we show that the first cohomology group of a logarithmic de Rham-Witt sheaf has a partial cycle module structure. As a consequence, we show that Kato complexes of logarithmic de Rham-Witt sheaves satisfy functoriality properties similar to Rost's cycle complexes.
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Updated on April 2, 2024
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