p-adic Hodge theory, anabelian conjecture, and arithmetic Simpson correspondence
p进霍奇理论、阿纳贝尔猜想和算术辛普森对应
基本信息
- 批准号:19K03401
- 负责人:
- 金额:$ 2.91万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2019
- 资助国家:日本
- 起止时间:2019-04-01 至 2024-03-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The project is about the crystalline comparison theorem in p-adic Hodge theory, with non-trivial coefficients and in the relative setting. During the research period, I studied in depth the work of Faltings and Scholze on integral p-adic Hodge theory. Currently I am able to formulate integral results for etale and crystalline cohomology with non-trivial coefficients. The relative version of such results shall need further investigation. The current theory of prismatic cohomology of Bhatt and Scholze seems to be the right way of formulating an integral comparison theorem with non-trivial coefficients. There has been some results in this direction, which generalizes my previous result published in 2019.
该项目是关于p进霍奇理论中的晶体比较定理,具有非平凡系数和相对设置。在研究期间,我深入研究了法尔明斯和肖尔茨关于积分p进霍奇理论的工作。目前,我能够制定积分的结果,etale和结晶上同调与非平凡的系数。这些结果的相关版本需要进一步调查。Bhatt和Scholze的棱柱上同调理论似乎是用非平凡系数建立积分比较定理的正确方法。在这个方向上已经有了一些结果,这概括了我之前在2019年发表的结果。
项目成果
期刊论文数量(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Crystalline comparison isomorphisms in p-adic Hodge theory: the absolutely unramified case
p-adic Hodge 理论中的晶体比较同构:绝对无分支的情况
- DOI:10.2140/ant.2019.13.1509
- 发表时间:2019
- 期刊:
- 影响因子:1.3
- 作者:Fucheng Tan;Jilong Tong
- 通讯作者:Jilong Tong
Some anabelian theorems
一些阿纳贝尔定理
- DOI:
- 发表时间:2019
- 期刊:
- 影响因子:0
- 作者:柳田伸太郎;Takehiro Hasegawa;安部利之;Fucheng Tan
- 通讯作者:Fucheng Tan
On Uchida's theorem and anabelian geometry of curves
论内田定理和阿贝尔曲线几何
- DOI:
- 发表时间:2019
- 期刊:
- 影响因子:0
- 作者:Miho Kitamura;Shintarou Yanagida;Fucheng Tan
- 通讯作者:Fucheng Tan
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上田 福大的其他文献
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