The Hyodo-Kato isomorphism for rational homotopy types

On p-adic comparison theorems for rigid analytic varieties, I

We compute, in a stable range, the arithmetic p-adic etale cohomology of smooth rigid analytic and dagger varieties (without any assumption on the existence of a nice integral model) in terms of differential forms using syntomic methods. The main technical input is a construction of a Hyodo-Kato cohomology and a Hyodo-Kato isomorphism with de Rham cohomology.

关于双塔中de Rham翻转的性质

On the de Rham flip-flopping in dual towers

本文研究了双塔中rigid分析空间的de Rham和Hyodo-Kato翻转性质，并展示了Drinfeld空间有限级覆盖的上同调作为$\mathbb{GL}_{d+1}(K)$的admissible表示。

域上刚性解析母题的一个权结构

A Weight Structure on Rigid Analytic Motives over a Field

本文通过伽罗瓦下降在局部域上刚性解析母题的稳定 ∞-范畴上构造幺半权结构，推广了 Binda-Gallauer-Vezzani 的好约化情形，并证明 Hyodo-Kato 实现经由权复形函子分解，从而得到收敛于 Hyodo-Kato 上同调的谱序列与权滤过。

关于$p$-进解析空间的上同调，I：基本比较定理

On the cohomology of $p$-adic analytic spaces, I: The basic comparison theorem

本文对$p$-进域代数闭包上的光滑刚性解析簇和dagger簇证明了基本$p$-进比较定理，将稳定范围内的pro-étale上同调表为de Rham上同调的滤过Frobenius特征空间，并通过完美oid空间范畴上的层实现了几何化。

On comparison between relative log de Rham-Witt cohomology and relative log crystalline cohomology

In this article, we prove the comparison theorem between the relative log de Rham-Witt cohomology and the relative log crystalline cohomology for a log smooth saturated morphism of fs log schemes satisfying certain condition. Our result covers the case where the base fs log scheme is etale locally log smooth over a scheme with trivial log structure or the case where the base fs log scheme is hollow, and so it generalizes the previously known results of Matsuue. In Appendix, we prove that our relative log de Rham-Witt complex and our comparison map are compatible with those of Hyodo-Kato.

Comparison between rigid syntomic and crystalline syntomic cohomology for strictly semistable log schemes with boundary

We introduce rigid syntomic cohomology for strictly semistable log schemes over a complete discrete valuation ring of mixed characteristic (0,p). In case a good compactification exists, we compare this cohomology theory to Nekovář-Nizioł's crystalline syntomic cohomology of the generic fibre. The main ingredients are a modification of Große-Klönne's rigid Hyodo-Kato theory and a generalisation of it for strictly semistable log schemes with boundary.