Coefficients in p-adic Hodge theory

p-adic Hodge 理论中的系数

• 批准号: 22KF0094
• 负责人: 辻 雄
• 金额: $ 1.47万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2023
• 资助国家: 日本
• 起止时间: 2023-03-08 至 2025-03-31
• 项目状态: 未结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22KF0094/
• 关键词: 相対Wach加群; 整p進表現; クリスタリン表現; p進局所系

研究員は学位論文の研究において，剰余体が完全な絶対不分岐なp進整数環上のsmoothな環の生成ファイバーの基本群の整p進表現に対して，絶対ガロア群の整p進表現に関するWach加群の理論を拡張した相対Wach加群の理論を構築し，相対Wach加群を持つ基本群の整p進表現はクリスタリン表現の格子となることを示していた．絶対ガロア群の整p進表現についてはすべてのクリスタリン表現の格子がWach加群を持つことが知られており，相対Wach加群でも同様の主張が成り立つかという基本的な問題が残されていた．クリスタリンp進表現の格子と局所自由性を緩めた絶対prismatic Fクリスタルの圏同値についての最近の先行研究を背景として，局所自由性を緩めた相対Wach加群を考えることにより，相対Wach加群の圏とクリスタリンp進表現の格子の圏のなす圏が圏同値になることを証明することに成功した．まず剰余体が完全でない絶対不分岐な完備離散付値環の場合に同様の定理を示し，それをp進整数環上のsmoothな環の特殊ファイバーの生成点に適用することにより上記結果を得た．前者については，類似のBreuil-Kisin加群において剰余体が完全な場合に帰着する先行研究があったが，Wach加群は群Γの作用を伴い，剰余体が完全な場合群Γは小さくなるため独自の工夫を要した．絶対prismatic Fクリスタルに関する上記先行研究との比較から，相対Wach加群への群Γの作用から対応するクリスタルを構成するためのstratificationを構成可能かという問題が自然に生ずる．この問題についても取り組み，相対Wach加群がある種の整p進周期環においてΓ作用が自明化されるという，絶対ガロア群の表現の場合にも知られていなかった新たな興味深い結果を得た．

The research staff have completed the study of the basic group of students in the smooth environment, and the whole group of students has been improved, and the whole group of students has been improved to show that there is no difference between the basic group of the smooth environment and the basic group of students in the smooth environment. Phase Wach adds the group to the whole group to show that the lattice is displayed. The group shows that the grid is displayed. The group shows that the lattice is Wach and the group is aware of the error. The basic problem of the Wach group is the same as that of the group. This is the basic problem of the general problem. This is the most important problem in the system. This is the most important thing in the case of the general situation. This is the most important thing in this paper. Recently, we have studied the background in the first place, and we have studied the background in the first place recently. We have studied the background in the first place, and the Wach in the group has been studied in the same way. In terms of Wach, we can see that the grid is in the same place. The remainder is complete, and there is no difference between them. In the whole number of numbers, the smooth environment special environmental information generation point has been obtained by using the results of the previous results. The former is similar to that of Breuil-Kisin, which is similar to that of the rest of the groups. in the first place, it is necessary to study the information in advance, and to add the partner of Wach to the cluster. The rest of the body is fully integrated with the group, so you need to spend a lot of time alone. You need to do some research in the first place. You need to do a lot of research in the first place. You can do a lot of research in the first place. In addition, you can add a group of people to improve your performance. The problem is that you may have a problem with stratification. The problem is that you can learn how to do it. Compared with the Wach group, the whole cycle is improved. The effect is self-evident. The group shows that the results show that the results are good.