Related papers: A Luna \'etale slice theorem for algebraic stacks

We prove a Slice Theorem around closed leaves in a singular Riemannian foliation, and we use it to study the $C^\infty$-algebra of smooth basic functions, generalizing to the inhomogeneous setting a number of results by G.~Schwarz. In…

Given a morphism from an affine semigroup Q to an arbitrary commutative monoid, it is shown that every fiber possesses an affine stratification: a partition into a finite disjoint union of translates of normal affine semigroups. The proof…

We develop a theory of good moduli spaces for derived Artin stacks, which naturally generalizes the classical theory of good moduli spaces introduced by Alper. As such, many of the fundamental results and properties regarding good moduli…

We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which…

Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of…

We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of M\"oller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in…

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 a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for…

We prove a relative GAGA theorem for perfect and pseudo-coherent complexes in non-archimedean analytic geometry, allowing bases given by Fredholm analytic rings, including those associated from affinoid perfectoid spaces. This answers a…

We prove that, under mild hypothesis, every normal algebraic space which satisfies the $1$-resolution property is quasi-affine. More generally, we show that for algebraic stacks satisfying similar hypotheses, the 1-resolution property…

Drinfeld's lemma is a powerful tool for splitting $\ell$-adic local systems defined over a product of connected schemes over a finite field. In this paper, we show that Drinfeld's lemma also holds true for algebraic stacks.

Given a compact Lie group $G$ acting on a space $X$, the classical Atiyah-Segal completion theorem identifies topological $K$-theory of the homotopy quotient $X/G$ with an explicit completion of $G$-equivariant topological $K$-theory of…

We show that the Hilbert functor of points on an arbitrary separated algebraic stack is an algebraic space. We also show the algebraicity of the Hilbert stack of points on an algebraic stack and the algebraicity of the Weil restriction of…

We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient…

The purpose of this note is to prove that there is an algebraic stack U parameterizing all curves. The curves that appear in the algebraic stack U are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also…

We prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient…

We extend the Galois-theoretic Borovoi-Springer interpretation of algebraic bands to a class of \'etale-locally represented bands on the fppf site of an arbitrary field $k$, which we call separable bands. Next, a band represented…

Cases of Deligne's companion conjecture for normal schemes over finite fields have been proven by L. Lafforgue, Drinfeld, and Zheng in recent years: L. Lafforgue proved the conjecture for curves, Drinfeld proved the conjecture for all…

We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…

This paper is focused on the structure of the Kauffman bracket skein algebra of a punctured surface at roots of unity. A criterion that determines when a collection of skeins forms a basis of the skein algebra as an extension over the…