Related papers: Overconvergent de Rham-Witt cohomology for semista…

We construct the relative log de Rham-Witt complex. This is a generalization of the relative de Rham-Witt complex of Langer-Zink to log schemes. We prove the comparison theorem between the hypercohomology of the log de Rham-Witt complex and…

For a strictly semistable log scheme $Y$ over a perfect field $k$ of characteristic $p$ we investigate the canonical \v{C}ech spectral sequence $(C)_T$ abutting to the Hyodo-Kato (log crystalline) cohomology $H_{crys}^*(Y/T)_{\mathbb{Q}}$…

In this paper, we prove the generic overconvergence of relative rigid cohomology with coefficient, by using the semistable reduction conjecture for overconvergent $F$-isocrystals (which is recently shown by Kedlaya).

We prove a comparison isomorphism between the De Rham rational homotopy type of a smooth proper log variety defined over a p-adic field and the crystalline rational homotopy type of a semi-stable reduction mod p.

The purpose of this article is to establish theories concerning $p$-adic analogues of Hodge cohomology and Deligne-Beilinson cohomology with coefficients in variations of mixed Hodge structures. We first study log overconvergent…

By exploring the geometric properties of Hyodo-Kato cohomology in rigid geometry, we establish several foundational results, including the semistable conjecture for \'etale cohomology of almost proper rigid analytic varieties, and GAGA…

We give a new and very intuitive construction of Hyodo--Kato cohomology and the Hyodo--Kato map, based on logarithmic rigid cohomology. We show that it is independent of the choice of a uniformiser and study its dependence on the choice of…

We build a unified framework for the study of monodromy operators and weight filtrations of cohomology theories for varieties over a local field. As an application, we give a streamlined definition of Hyodo-Kato cohomology without recourse…

In this paper, we develop the theory of relative log convergent cohomology. We prove the coherence of relative log convergent cohomology in certain case by using the comparison theorem between relative log convergent cohomlogy and relative…

We generalize the functorial quasi-isomorphism in \cite{Davis2011} from overconvergent Witt de-Rham cohomology to rigid cohomology on smooth varieties over a finite field $k$, dropping the quasi-projectiveness condition. We do so by…

Let X be a smooth variety over a perfect field of characteristic p>0. In this small note we define overconvergent F-de Rham-Witt connections as an analogue for F-crystals over proper schemes. We prove that the forgetful functor from the…

We explain how to construct a cohomology theory on the category of separated quasi-compact smooth rigid spaces over $\mathbf{C}_p$ (or more general base fields), taking values in the category of vector bundles on the Fargues-Fontaine curve,…

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…

We construct log-motivic cohomology groups for semistable varieties and study the $p$-adic deformation theory of log-motivic cohomology classes. Our main result is the deformational part of a $p$-adic variational Hodge conjecture for…

By works of Kedlaya and Shiho, it is known that, for a smooth variety $\overline{X}$ over a field of positive characteristic and its simple normal crossing divisor $Z$, an overconvergent isocrystal on the compliment of $Z$ satisfying a…

Let $k$ be a perfect field of positive characteristic and $Z$ an effective Cartier divisor in the projective line over $k$ with complement $U$. In this note, we establish some results about the formal deformation theory of overconvergent…

Let A be a finitely generated algebra over a field K of characteristic p >0. We introduce a subring of the ring of Witt vectors W(A). We call it the ring of overconvergent Witt vectors. We prove that on a scheme X of finite type over K the…

We prove the semistable reduction theorem for $\mathcal{E}^{\dag}_K$-valued and $K$-valued overconvergent $F$-isocrystals over $k((t))$-varieties which were introduced by Lazda and P\'{a}l. As an application, we prove the finite…

In this paper, we develop the theory of relative log convergent cohomology of radius $\lambda$ ($0 < \lambda \leq 1$), which is a generalization of the notion of relative log convergent cohomology in the previous paper. By comparing this…

We prove that, for adic \'{e}tale motives over $\mathbb{C}_p$, the vector bundles on the Fargues-Fontaine curve arising from their Hyodo-Kato cohomology coincide with their de Rham-Fargues-Fontaine cohomologies, where the latter provides an…