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| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
2019年11月27日(水)
17:00-18:00 数理科学研究科棟(駒場) 117号室
Ahmed Abbes 氏 (CNRS & IHÉS)
The relative Hodge-Tate spectral sequence (ENGLISH)
Ahmed Abbes 氏 (CNRS & IHÉS)
The relative Hodge-Tate spectral sequence (ENGLISH)
[ 講演概要 ]
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. But the generalization of the Hodge-Tate spectral sequence to a relative situation has not yet been considered (not even conjectured), with the exception of a special case of abelian schemes by Hyodo. This has now been done in a joint work with Michel Gros. The relative Hodge-Tate spectral sequence that we construct takes place in the Faltings topos, but 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.
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. But the generalization of the Hodge-Tate spectral sequence to a relative situation has not yet been considered (not even conjectured), with the exception of a special case of abelian schemes by Hyodo. This has now been done in a joint work with Michel Gros. The relative Hodge-Tate spectral sequence that we construct takes place in the Faltings topos, but 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.
