Related papers: The relative Hodge-Tate spectral sequence for rigi…

We construct a K-theory version of Bhatt-Morrow-Scholze's Breuil-Kisin cohomology theory for $\sO_K$-linear idempotent-complete, small smooth proper stable infinity-categories, where $K$ is a discretely valued extension of $\Q_p$ with…

The primary goal of this paper is to identify syntomic complexes with the $p$-adic \'etale Tate twists of Geisser--Schneider--Sato on regular $p$-torsionfree schemes. Our methods apply naturally to a broader class of schemes that we call…

Let $(M,g)$ be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian $\Delta$ is essentially self-adjoint. We establish the…

We introduce higher analytic geometry, a novel framework extending Lurie's derived complex analytic spaces. This theory generalizes classical complex analytic geometry, enabling the study of derived K\"ahler spaces with non-trivial higher…

We construct a Grothendieck-Witt space for any stable infinity category with duality. If we apply our construction to perfect complexes over a commutative ring in which 2 is invertible we recover the classical Grothendieck-Witt space. Our…

The geometry of the Lubin-Tate space of deformations of a formal group is studied via an \'etale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of…

We give an example of proper smooth fourfold over a perfect field k of characteristic p > 0 with asymmetric Hodge--Witt numbers in total degree 3. Our example is sharp both in terms of dimension and total degree. We arrive at our example by…

We study the Hodge-to-de Rham spectral sequence for integral projective curves with local complete intersection singularities. We prove that degeneration at the E2-page is equivalent to requiring every singularity to be a quasihomogeneous…

In this paper, we establish an innovative framework in logarithmic Hodge theory for toroidal varieties, introducing weighted toroidal structures and developing a systematic obstruction theory for Hodge classes. Building upon recent advances…

We establish a Grothendieck--Lefschetz theorem for smooth ample subvarieties of smooth projective varieties over an algebraically closed field of characteristic zero and, more generally, for smooth subvarieties whose complement has small…

We give an elementary short proof of Grothendieck's base change theorem for the cohomology of flat coherent sheaves.

We study $p$-adic Hodge theory for families of Galois representations over pseudorigid spaces. Such spaces are non-archimedean analytic spaces which may be of mixed characteristic, and which arise naturally in the study of eigenvarieties at…

We prove a number of results on the \'etale cohomology of rigid analytic varieties over $p$-adic non-archimedean local fields. Among other things, we establish bounds for Frobenius eigenvalues, show a strong version of Grothendieck's local…

We prove a Hodge-type decomposition for the de-Rham cohomology of $ p$-adically uniformized varieties by the product of Drinfeld's symmetric spaces. It is based on work of Schneider, Stuhler, Iovita and Spiess on the cohomology of…

We introduce the notion of relative pseudocoefficient for relative discrete series of real spherical homogeneous spaces of reductive groups. We prove that such relative pseudocoefficient does not exist for semisimple symmetric spaces of…

Motivated by applications in point counting algorithms using p-adic cohomology, we give an explicit description of integral lattices in rigid cohomology spaces that p-adically approximate logarithmic crystalline cohomology modules. These…

In this short note we show that the homotopy category of smooth compactifications of smooth algebraic varieties is equivalent to the homotopy category of smooth varieties over a field of characteristic zero. As an application we show that…

We describe the obstruction to decomposing in degrees $\leq p$ the de Rham complex of a smooth variety over a perfect field $k$ of characteristic $p$ that lifts over $W_2(k)$, and show that there exist liftable smooth projective varieties…

We relate various approaches to coefficient systems in relative integral $p$-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over…

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,…