Related papers: p-adic derived de Rham cohomology

In this paper, we consider the (crystalline) prismatic crystals on a scheme $\mathfrak{X}$. We classify the crystals by $p$-connections on a certain ring and prove a cohomological comparison theorem. This equivalence is more general than…

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…

We show that the direct image of the filtered logarithmic de Rham complex is a direct sum of filtered logarithmic complexes with coefficients in variations of Hodge structures, using a generalization of the decomposition theorem of…

We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra,…

In 1989, Faltings proved the comparison theorem between \'etale cohomology and crystalline cohomology by studying Fontaine-Faltings modules and crystalline representations. In his paper, he mentioned these modules and representations can be…

Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…

We develop a new cohomology theory in characteristic p>0, the so called F-gauge cohomology, a cohomology with values in the category of so-called F-gauges, which refines the cristalline cohomology. In this first paper we mainly discuss the…

We compute the p-adic geometric \'etale cohomology of the coverings of Drinfeld's half-plane, and we show that, if the base field is Q_p, this cohomology encodes the p-adic local Langlands correspondence for 2-dimensional de Rham…

We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals. This extension accommodates, in…

For complex parallelisable manifolds $\Gamma\backslash G$, with $G$ a solvable or semisimple complex Lie group, the Fr\"olicher spectral sequence degenerates at the second page. In the solvable case, the de-Rham cohomology carries a pure…

We investigate $p$-adic cohomologies of log rigid analytic varieties over a $p$-adic field. For a log rigid analytic variety $X$ defined over a discretely valued field, we compute the Kummer pro-\'etale cohomology of…

It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the…

For a smooth and proper scheme over an artinian local ring with ordinary reduction over the perfect residue field we prove - under some general assumptions - that the relative de Rham-Witt spectral sequence degenerates and the relative…

In this note, we prove the logarithmic $p$-adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal crossing divisor is locally $K(\pi,1)$ (in a certain sense) with…

This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.

For a locally nilpotent integrable connection on a proper (strict) semistable family over a small polydisc with a relative horizontal simple normal crossing divisor, we construct a canonical section in derived categories inducing an…

Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd…

The first part of the paper is a survey of recent results about the cohomology of $(\phi,\Gamma)$-modules and its applications to the theory of Selmer complexes. In the second part we formulate a version of the Main Conjecture for $p$-adic…

We describe algebraically defined cohomological and homological Albanese and Picard 1-motives (or mixed motives) of any algebraic variety in characteristic zero, generalizing the classical Albanese and Picard varieties. We compute Hodge,…

This paper provides the technical tools needed in ongoing work of the authors to compute p-adic \'etale Abel-Jacobi maps in order to obtain explicit reciprocity laws for GSp4. In particular, we define and study syntomic polynomial…