On the continuity of the finite Bloch–Kato cohomology
Adrian Iovita
Università di Padova, ItalyAdriano Marmora
Université de Strasbourg, France
![On the continuity of the finite Bloch–Kato cohomology cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rsmup-volume-134.png&w=3840&q=90)
Abstract
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 .
Cite this article
Adrian Iovita, Adriano Marmora, On the continuity of the finite Bloch–Kato cohomology. Rend. Sem. Mat. Univ. Padova 134 (2015), pp. 239–271
DOI 10.4171/RSMUP/134-6