We describe the mod p(r) pro K-groups {K-n, (A/I-s)/p(r)}(s) of a regular local F-p-algebra A modulo powers of a suitable ideal I, in terms of logarithmic Hodge-Witt groups, by proving pro analogues of the theorems of Geisser-Levine and Bloch-Kato-Gabber. This is achieved by combining the pro Hochschild-Kostant-Rosenberg theorem in topological cyclic homology with the development of the theory of de Rham-Witt complexes and logarithmic Hodge-Witt sheaves on formal schemes in characteristic p.
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