Let be an unramified, complete discrete valuation field of mixed characteristics with perfect residue field. We consider two finite, free -representations of , and , such that , for , are crystalline representations with Hodge-Tate weights between and Let be a totally ramified extension of degree of . Supposing that and , we prove that for every integer and , the inclusion of the finite Bloch-Kato cohomology into the Galois cohomology is functorial with respect to morphisms as -modules from to . In the appendix we give a related result for .
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Adrian Iovita, Adriano Marmora, On the continuity of the finite Bloch–Kato cohomology. Rend. Sem. Mat. Univ. Padova 134 (2015), pp. 239–271DOI 10.4171/RSMUP/134-6