相关论文: Flat descent for Artin n-stacks

The purpose of this paper is to lay the foundations of a theory of invariants in \'etale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get…

We propose a generalization of Artin's definition of algebraic stack, which we call {\em geometric $n$-stack}. The main observation is that there is an inductive structure to the definition whereby the ingredients for the definition of…

This is a sequel of our previous work, arXiv:2209.09686, on the development of derived contact geometry, in which we formally introduced shifted contact structures on derived stacks and proved some results for $k$-shifted contact derived…

We prove Artin's axioms satisfy a compatibility for composition of 1-morphisms of stacks in groupoids. Consequently, some natural stacks in groupoids are algebraic, including a common generalization of Vistoli's Hilbert stack and the stack…

We prove several results on the model theory of Artin groups, focusing on Artin groups which are ``far from right-angled Artin groups''. The first result is that if $\mathcal{C}$ is a class of Artin groups whose irreducible components are…

We discuss log flat topology and log flat descents of log schemes

We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a smooth quasi-projective variety over the Fargues-Fontaine curve. Namely, we show how to use their criterion to deduce an analogue for spaces…

The purpose of this article is to study the role of Artin fans in tropical and non-Archimedean geometry. Artin fans are logarithmic algebraic stacks that can be described completely in terms of combinatorial objects, so called Kato stacks,…

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…

Let $K$ be a finite extension of $\mathbb{Q}_p$. We prove that the arithmetic $p$-adic pro-\'etale cohomology of smooth partially proper spaces over $K$ satisfies a duality, as conjectured by Colmez, Gilles and Nizio{\l}. We derive it from…

Given a liftable smooth proper variety over $\mathbb{F}_p$, we construct the moduli stacks of crystals and isocrystals on it. We show that the former is a formal algebraic stack over $\mathbb{Z}_p$ and the latter is an adic stack -- Artin…

The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over $\mathbb{C} ^n$ is not well-understood except for $n=1$. We present four examples of smooth affine algebraic hypersurfaces that…

This work is devoted to the study of integral $p$-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of $p$-adic Hodge theory with the \'etale…

We study the descent behaviour of homotopy-theoretic properties of smooth complex affine surfaces under finite surjective morphisms. We first examine the Eilenberg-MacLane property and show, by means of an explicit counterexample, that it…

This paper is a continuation of our earlier development of a theory of tame Artin stacks. Our main goal here is the construction of an appropriate analogue of Kontsevich's space of stable maps in the case where the target is a tame Artin…

We present a collection of conjectural trace identities and explain why they are equivalent to base change and descent of automorphic representations of $\mathrm{GL}_n(\mathbb{A}_F)$ along nonsolvable extensions (under some simplifying…

We construct finite-dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Lie algebra together with a Dynkin diagram automorphism. We…

We extend results about $n$-shifted coisotropic structures from part I of this work to the setting of derived Artin stacks. We show that an intersection of coisotropic morphisms carries a Poisson structure of shift one less. We also compare…

The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA always admit a faithful action by automorphisms of a…

In this paper we give a construction of algebraic (Artin) stacks endowed with a modular map onto the moduli stack of n-pointed stable curves of genus g, for g greater than 2. These stacks are smooth, irreducible and have dimension 4g-3+n,…