论文标题
$ p $ - adic动机的几何和代表理论方面
Geometric and Representation Theoretic Aspects of $p$-adic Motives
论文作者
论文摘要
在本文中，我们主要讨论了相对$ p $ - 亚种霍奇理论和$ p $ - 亚种动机的相应几何和表示理论方面。 To be more precise, we study the corresponding analytic geometry of the corresponding spaces over and attached to period rings in the relative $p$-adic Hodge theory, including derived topological de Rham complexes and derived topological logarithmic de Rham complexes after Bhatt, Gabber, Guo and Illusie which is in some sense equivalent to the derived prismatic cohomology of Bhatt-Scholze as shown in the work of li-liu，$ \ mathcal {o} \ mathbb {b} _ \ mathrm {dr} $ - sheaves scholze，$φ$ - $ \ $ \ wideTilde {c} _x $ - sheaves _x $ - sheaeves and相对 - $ b $ - kedlaya-liimensional andry andry andry andry andring carersion-carter-after-after-after-after-after-after multymensional-carersion-carersion-carersion-carertring-carter-carter-carerter mings-- Pal-Zábrádi和许多其他可能的通用通用动机或滑轮。预计将通过使用Quasiregular semiperfecoids使用Quasiregular semiperfectoids，如Bhatt-Morrow-Morrow-Scholze和Bhatt-Scholze的工作，预计将通过使用完美的分析空间或Quasisyntomic位点来融合许多环境。
In this dissertation, we discuss mainly the corresponding geometric and representation theoretic aspects of relative $p$-adic Hodge theory and $p$-adic motives. To be more precise, we study the corresponding analytic geometry of the corresponding spaces over and attached to period rings in the relative $p$-adic Hodge theory, including derived topological de Rham complexes and derived topological logarithmic de Rham complexes after Bhatt, Gabber, Guo and Illusie which is in some sense equivalent to the derived prismatic cohomology of Bhatt-Scholze as shown in the work of Li-Liu, $\mathcal{O}\mathbb{B}_\mathrm{dR}$-sheaves after Scholze, $φ$-$\widetilde{C}_X$-sheaves and relative-$B$-pairs after Kedlaya-Liu, multidimensional rings after Carter-Kedlaya-Zábrádi and Pal-Zábrádi and many other possible general universal motivic rings or sheaves. Many contexts are expected to be sheafified, such as over Scholze's pro-étale sites of the considered analytic spaces by using perfectoids or the quasisyntomic sites by using quasiregular semiperfectoids as in the work of Bhatt-Morrow-Scholze and Bhatt-Scholze.
