We study a Grothendieck topology on schemes which we call the arc-topology. This
topology is a refinement of the v-topology (the pro-version of Voevodsky'sh-topology), where …

We prove that torsors under parahoric group schemes on the punctured spectrum of
Fontaine's ring A inf, extend to the whole spectrum. Using descent we can extend a similar …

We review the theory of almost coherent modules that was introduced in" Almost Ring
Theory" by Gabber and Ramero. Then we globalize it by developing a new theory of almost …

We develop a 6-functor formalism $\mathcal {D} _ {[0,\infty)}(-) $ with $\mathbb {Z} _p $-
linear coefficients on small v-stacks, and discuss consequences for duality and finiteness for …

We develop a theory of log adic spaces by combining the theories of adic spaces and log
schemes, and study the Kummer étale and pro-Kummer étale topology for such spaces. We …

We prove a generic smoothness result in rigid analytic geometry over a characteristic zero
non-archimedean field. The proof relies on a novel notion of generic points in rigid analytic …

In this paper, we address two conjectures about the rigid-analytical analogues of the Artin--
Grothendieck Vanishing Theorem. First, we show the remaining cases of the Artin …

We prove that torsors under parahoric group schemes on the punctured spectrum of
Fontaine's ring $ A_ {\mathrm {inf}} $, extend to the whole spectrum. Using descent we can …

Sen's theorem on the ramification of a $ p $-adic analytic Galois extension of $ p $-adic local
fields shows that its perfectoidness is equivalent to the non-vanishing of its arithmetic Sen …

We develop the notion of a geometric covering of a rigid space 𝑋, which yields a larger class
of covering spaces than that studied previously by de Jong. Geometric coverings are closed …