【online】The relative Hodge-Tate spectral sequence
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题目：The relative Hodge-Tate spectral sequence
报告人：Ahmed Abbes （法国高等科学研究所（IHES））
报告方式：Zoom会议 ID：842 2144 4288 密码: 854848
摘要：It is well known that the p-adic étale cohomology of a smooth and proper variety over a p-adic field admits a Hodge-Tate decomposition and that it is the abutment of a spectral sequence called Hodge-Tate; these two properties are incidentally equivalent. The Hodge-Tate decomposition was generalized in higher dimensions to Hodge-Tate local systems by Hyodo, and was studied by Faltings, Tsuji and others. I will report on a joint work with Michel Gros providing a generalization of the Hodge-Tate spectral sequence to morphisms. The latter takes place in Faltings topos. Its construction requires the introduction of a relative variant of this topos which is the main novelty of our work. The relative Hodge-Tate spectral sequence sheds new light on the fact that the relative p-adic étale cohomology is Hodge-Tate, but the two properties are not equivalent in general.