Related papers: Coherently complete algebraic stacks in positive c…

We prove the algebraicity of the Hilbert functor, the Hilbert stack, the Quot functor and the stack of coherent sheaves on an algebraic stack X with (quasi-)finite diagonal without any finiteness assumptions on X. We also give similar…

We study the general and connected stable ranks for $C^{\ast}$-algebras. We estimate these ranks for certain $C(X)$-algebras, and use that to do the same for certain group $C^{\ast}$-algebras. Furthermore, we also give estimates for the…

Let $A$ be a central quantization of an affine Poisson variety $X$ over a field of characteristic $p>0.$ We show that the completion of $A$ with respect to a closed point $y\in X$ is isomorphic to the tensor product of the Weyl algebra with…

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-$\mathcal{C}$ completions of the…

We study the limits of inductive sequences (A_i,\phi_i) where each A_i is a direct sum of full matrix algebras over compact metric spaces and each partial map of \phi_i is diagonal. We give a new characterisation of simplicity for such…

We give another proof that a reductive algebraic group is geometrically reductive. We show that a quotient of the semi-stable locus (by a linear action of a reductive algebraic group on a projective scheme) exists, and from this Haboush's…

In this short article, given a smooth diagonalizable group scheme G of finite type acting on a smooth quasi-compact quasi-separated scheme X, we prove that (after inverting some elements of representation ring of G) all the information…

We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative…

Let $G$ be an infinite discrete group. A classifying space for proper actions of $G$ is a proper $G$-CW-complex $X$ such that the fixed point sets $X^H$ are contractible for all finite subgroups $H$ of $G$. In this paper we consider the…

The objective of this paper is to introduce and study completions and local homology of comodules over Hopf algebroids, extending previous work of Greenlees and May in the discrete case. In particular, we relate module-theoretic to…

Let $G$ be a locally compact, Hausdorff, second countable groupoid and $A$ be a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant,…

We prove a decomposition theorem for the equivariant K-theory of actions of affine group schemes G of finite type over a field on regular separated noetherian algebraic spaces, under the hypothesis that the actions have finite geometric…

We prove finite generation of the algebra of type A conformal blocks over arbitrary stable curves of any genus. As an application we construct a flat family of irreducible normal projective varieties over the moduli stack of stable pointed…

We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…

Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic $p \ge 0$. We give a case-free proof of Lusztig's conjectures [Unipotent elements in small characteristic, {\em Transform. Groups} 10…

We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes…

We prove that cohomology and base change holds for algebraic stacks, generalizing work of Brochard in the tame case. We also show that Hom-spaces on algebraic stacks are represented by abelian cones, generalizing results of Grothendieck,…

A topological gyrogroup is a gyrogroup endowed with a compatible topology such that the multiplication is jointly continuous and the inverse is continuous. In this paper, we study the quotient gyrogroups in topological gyrogroups with…

The Akbari-Cameron-Khosrovshahi (ACK) conjecture, which appears to be unresolved, states that for any simple graph $G$ with at least one edge, there exists a nonzero {$\{0,1\}$}-vector in the row space of its adjacency matrix that is not a…

Raynaud--Gruson characterized flat and pure morphisms between affine schemes in terms of projective modules. We give a similar characterization for non-affine morphisms. As an application, we show that every quasi-coherent sheaf is the…