Related papers: Note on local structure of Artin stacks

We give criteria for a graph of groups to have finite stature with respect to its collection of vertex groups, in the sense of Huang-Wise. We apply it to the triangle Artin groups that were previously shown to split as a graph of groups.…

We show that if a flat group scheme acts properly, with finite stabilizers, on an algebraic space, then a quotient exists as a separated algebraic space. More generally we show any flat groupid for which the family of stabilizers is finite…

For a family of principal bundles with a reductive structure group on a family of curves in characteristic zero, it is known that the Harder Narasimhan type of its restriction to each fiber varies semicontinuously over the parameter scheme…

For a derived stack obtained as a quotient of a derived affine scheme by a reductive group, we show that shifted symplectic structures can be characterized by the Cartan-de Rham complex. For non-reductive groups, we also show the analogous…

We prove that a group acting geometrically on a thick affine building has property (T). A more general criterion for property (T) is given for groups acting on partite complexes.

In this paper we characterise the action of the absolute Galois group on the geometric finite cyclic groups without \'etale factorization of stack inertia of the profinite geometric fundamental group of moduli spaces of marked curves. As a…

We prove the $K(\pi,1)$ conjecture for affine Artin groups: the complexified complement of an affine reflection arrangement is a classifying space. This is a long-standing problem, due to Arnol'd, Pham, and Thom. Our proof is based on…

Following Serre's initial work, a number of authors have considered twists of quadratic forms on a scheme Y by torsors of a finite group G, together with formulas for the Hasse-Witt invariants of the twisted form. In this paper we take the…

In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.

We prove that every $0$-shifted Poisson structure on a derived Artin $n$-stack admits a curved $A_{\infty}$ deformation quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes, where it…

We provide a complete description of the presentations of the interval groups related to quasi-Coxeter elements in finite Coxeter groups. In the simply laced cases, we show that each interval group is the quotient of the Artin group…

We show that on integral normal separated schemes whose function field is separably closed, for each pair of points the intersection of the resulting local schemes is local. This extends a result of Artin from rings to schemes. The argument…

We define a functorial "Artin map" attached to any small $\bf{Z}$-linear stable $\infty$-category, which in the case of perfect complexes over a global field recovers the usual Artin map from the idele class group to the abelianized…

We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true but no written proof was…

This paper verifies Abhyankar's Inertia Conjecture for certain sporadic groups $G$ in particular characteristics by showing that all possible inertia groups occur for $G$-Galois covers of the affine line. For a larger set of sporadic…

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…

We prove that every variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. We additionally prove new McKay correspondences for resolutions by Artin stacks, expressing stringy invariants of…

In this short note, we prove a purity result for crystalline local systems on a smooth $p$-adic affine formal scheme. Our method is based on the prismatic description of crystalline local systems.

Let X_1 and X_2 be mixing connected algebraic dynamical systems with the Descending Chain Condition. We show that every equivariant continuous map X_1 to X_2 is affine (that is, X_2 is topologically rigid) if and only if the system X_2 has…

Given a number field $F$ with $\o_F$ its ring of integers. For certain $a,b$ and $\alpha$ in $\o_F$, we show that the Artin condition is the only obstruction to the local-global principle for integral solutions of equation…