Related papers: Artin vanishing in rigid analytic geometry

Artin vanishing theorems for Stein spaces refer to the vanishing of some of their (co)homology groups in degrees higher than the dimension. We obtain new positive and negative results concerning Artin vanishing for the cohomology of a Stein…

First, we prove an algebraization result for rig-smooth algebras over a general noetherian ring; this positively answers the question raised in [Sta24, Tag 0GAX]. Then we prove a general partial algebraization result in non-archimedean…

In this article, we study the cohomology of some analytic sheaves on the complementary in the projective space of a suitable infinite collection of hyperplane like the Drinfel'd symetric space. In particular, the sheaf of invertible…

We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely valued field, its continuous K-groups vanish in degrees below the negative of the…

We prove, for quasicompact separated schemes over ground fields, that Cech cohomology coincides with sheaf cohomology with respect to the Nisnevich topology. This is a partial generalization of Artin's result that for noetherian schemes…

Full level-n structures on smooth, complex curves are trivializations of the n-torsion points of their Jacobians. We give an algebraic proof that the etale cohomology of the moduli space of smooth, complex curves of genus at least 2 with…

Among other things, we show that the ideal sheaf of a complex Hilbert submanifold of a pseudoconvex open subset of Hilbert space is acyclic over the ambient pseudoconvex open set. We also prove a vanishing theorem for a fairly general class…

Let $X$ be a smooth connected projective algebraic curve over an algebraically closed field, and let $S$ be a finite nonempty closed subset in $X$. We study deformations of $\overline{\mathbb F}_\ell$-sheaves. The universal deformation…

Let $K$ be a field of characteristic zero complete with respect to a non-trivial, non-Archimedean valuation. We relate the sheaf $\widehat{\mathcal{D}}$ of infinite order differential operators on smooth rigid $K$-analytic spaces to the…

Let $k$ be a non-archimedean complete valued field and $X$ be a $k$-analytic space in the sense of Berkovich. In this note, we prove the equivalence between three properties: 1) for every complete valued extension $k'$ of $k$, every…

We provide a complete proof of a duality theorem for the fppf cohomology of either a curve over a finite field or a ring of integers of a number field, which extends the classical Artin-Verdier Theorem in \'etale cohomology. We also prove…

We study a Grothendieck topology on schemes which we call the $\mathrm{arc}$-topology. This topology is a refinement of the $v$-topology (the pro-version of Voevodsky's $h$-topology) where covers are tested via rank $\leq 1$ valuation…

We develop a theory of nearby and vanishing cycles in the context of finite-coefficient Zariski-constructible sheaves over a non-archimedean field which is non-trivially valued, complete, algebraically closed, and of mixed characteristic or…

On Zariski Main Theorem in Algebraic Geometry and Analytic Geometry. We fill a surprising gap of Complex Analytic Geometry by proving the analogue of Zariski Main Theorem in this geometry, i.e. proving that an holomorphic map from an…

We explain how any Artin stack $\mathfrak{X}$ over $\mathbb{Q}$ extends to a functor on non-negatively graded commutative cochain algebras, which we think of as functions on Lie algebroids or stacky affine schemes. There is a notion of…

The cohomology of coherent sheaves and sheaves of Abelian groups on Noetherian schemes are interpreted in second order arithmetic by means of a finiteness theorem. This finiteness theorem provably fails for the etale topology even on…

I extend the framework of rigid analytic geometry to the setting of algebraic geometry relative to monoids, and study the associated notions of separated, proper, and overconvergent morphisms. The category of affine manifolds embeds as a…

We introduce a class of analytic sheaves in a Banach space X, that we call cohesive sheaves. Cohesion is meant to generalize the notion of coherence from finite dimensional analysis. Accordingly, we prove the analog of Cartan's Theorems A…

We prove that the cohomology of the integral structure sheaf of a normal affinoid adic space over a non-archimedean field of characteristic zero is uniformly torsion. This result originated from a remark of Bartenwerfer around the 1980s and…

We prove the generic base change theorem for stacks, and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables…