Related papers: Quotients of complex algebraic supergroups

It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a…

Moerdijk's site description for equivariant sheaf toposes on open topological groupoids is used to give a proof for the (known, but apparently unpublished) proposition that if H is a strictly full subgroupoid of an open topological groupoid…

In this article, we show that if $X$ is an excellent surface with rational singularities, the constant sheaf $\mathbb{Q}_{\ell}$ is a dualizing complex. In coefficient $\mathbb{Z}_{\ell}$, we also prove that the obstruction for…

We introduce a concept that we call module restriction, which generalizes the classical Weil restriction. We first establish some fundamental properties, as existence and \'etaleness. Then we apply our results to show that Grothendiecks…

We define a sheaf of abelian groups whose cohomology is represented by the cotangent complex. We show how obstructions to some standard deformation problems arise as the classes of torsors under and gerbes banded by this sheaf.

We display a symmetric monoidal equivalence between the stable $\infty$-category of filtered spectra, and quasi-coherent sheaves on $\mathbb{A}^1 / \mathbb{G}_m$, the quotient in the setting of spectral algebraic geometry, of the flat…

We introduce ``sheafification'' functors from categories of (lax monoidal) linear functors to categories of quasi-coherent sheaves (of algebras) of stacks. They generalize the homogeneous sheafification of graded modules for projective…

The problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group to the algebra of sections of a sheaf of…

The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control of the norms, without any of the smoothness assumptions that…

In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In…

We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…

We prove embeddings of adelic groups on an excellent scheme of special type and a flat quasicoherent sheaf on it. For a normal excellent scheme of special type we establish the equality…

We give the definitions of affine algebraic supervariety and affine algebraic group through the functor of points and we relate them to the other definitions present in the literature. We study in detail the algebraic supergroup $SL(m|n)$…

For a reductive group $G$ over a ring $A$, its affine Grassmannian $\mathrm{Gr}_G$ plays important roles in a wide range of subjects and is typically defined as the \'etale sheafification of the presheaf quotient $LG/L^+G$ of the loop group…

Let $S$ be a noetherian scheme, and let $E$ be a coherent sheaf on it. We define a group-valued contravariant functor $GL_E$ on $S$-schemes by associating to any $S$-scheme $T$ the group $GL_E(T)$ of all linear automorphisms of the pullback…

We study equivariant sheaves over profinite spaces, where the group is also taken to be profinite. We resolve a serious deficit in the existing theory by constructing a good notion of equivariant presheaves, with a suitable equivariant…

We prove that every filtered fiber functor on the category of dualizable representations of a smooth affine group scheme with enough dualizable representations comes from a graded fiber functor.

In this paper, we study K-theory of spectral schemes by using locally free sheaves. Let us regard the K-theory as a functor K on affine spectral schemes. Then, we prove that the group completion $\Omega B^{\mathcal{G}}(B^{\mathcal{G}}GL)$…

We generalize to the super context, the known fact that if an affine algebraic group $G$ over a commutative ring $k$ acts freely (in an appropriate sense) on an affine scheme $X$ over $k$, then the dur sheaf $X\tilde{\tilde{/}}G$ of…

We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morphism. Using this notion of morphism, we obtain (higher)…