Related papers: Logarithmic adic spaces: some foundational results

We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmueller theory, and illustrate how a wide range of…

We compute the cohomology of the right generalised projective Stiefel manifolds and use it to find bounds on the rank of the complementary bundle for certain vector bundles. Further the cohomology computations are also used to find bounds…

We compute the Hodge and de Rham cohomology of the classifying space BG (defined as etale cohomology on the algebraic stack BG) for reductive groups G over many fields, including fields of small characteristic. These calculations have a…

We discuss recent developments in $p$-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact $p$-adic manifolds" over new period maps on moduli spaces of abelian…

In this paper, we record some foundational results on adic geometry that seem to be missing in the existing literature. Namely, we develop the Proj construction and a theory of lci closed immersions in the context of locally noetherian…

In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…

We establish a structure theorem on the arc space of a $k$-scheme of finite type. More precisely, we show that the arc space is locally for the pro-smooth toplogy a product of an infinite dimensional affine space and of a non-noetherian…

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision…

We construct the $\Lambda$-adic crystalline and Dieudonn\'e analogues of Hida's ordinary $\Lambda$-adic \'etale cohomology, and employ integral $p$-adic Hodge theory to prove $\Lambda$-adic comparison isomorphisms between these cohomologies…

We study the cohomology of the group of rational points of a linear algebraic group on adelic functional spaces, and we explore the relation with Emerton's completed cohomology.

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…

We introduce a Zariskian analogue of the theory of Huber's adic spaces.

We explain how results comparing the homology of spaces of algebraic and continuous maps to projective spaces can be leveraged to compare moduli stacks of families of algebraic and continuous maps.

We describe in elementary geometrical terms Teichm\" uller spaces of decorated and holed surfaces. We construct explicit global coordinates on them as well as on the spaces of measured laminations with compact and closed support…

We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an \'etale topological realization of the stable motivic homotopy theory of smooth schemes over a base…

We study three different topologies on the moduli space $\mathscr{H}^{\rm loc}_m$ of equivariant isometry classes of $m$-dimensional locally homogeneous Riemannian spaces. As an application, we provide the first examples of locally…

We prove an analogue of Scholze's Primitive Comparison Theorem for proper rigid spaces over an algebraically closed non-archimedean field $K$ of characteristic $p$. This implies a v-topological version of the Primitive Comparison Theorem…

Let $\mathcal{H}^{n-1}_{K}$ denote the $(n-1)$-dimensional Drinfeld space over a $p$-adic field $K$. We give an explicit description of the $\ell$-adic and $p$-adic pro-\'etale cohomology of quotient stacks…

K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite…