Kato complexes of reciprocity sheaves and applications

Abstract

We show that every reciprocity sheaf gives rise to a cycle (pre)module in the sense of Rost over a perfect field, under mild additional hypotheses. 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.