Related papers: Effective models of group schemes

Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or…

For a connected reductive group G and a finite-dimensional G-module V, we study the invariant Hilbert scheme that parameterizes closed G-stable subschemes of V affording a fixed, multiplicity-finite representation of G in their coordinate…

Given an affine scheme X with an action of a reductive group G and a G-linearized coherent sheaf M, we construct the ``invariant Quot scheme'' that parametrizes the quotients of M whose space of global sections is a direct sum of simple…

Let G be a finite group acting tamely on a proper reduced curve C over an algebraically closed field. We study the G-module structure on the cohomology groups of a G-equivariant locally free sheaf F on C, and give formulas of…

For a semi-stable abelian variety A_K over a complete discrete valuation field K, we show that every finite subgroup scheme of A_K extends to a log finite flat group scheme over the valuation ring of K endowed with the canonical log…

Let $R$ be a discrete valuation ring of field of fractions $K$ and of residue field $k$ of characteristic $p > 0$. In an earlier work, we studied the question of extending torsors on $K$-curves into torsors over $R$-regular models of the…

Let $K$ be a field and $G$ be a group of its automorphisms endowed with the compact-open topology. There are many situations, where it is natural to study the category $Sm_K(G)$ of smooth (i.e. with open stabilizers) $K$-semilinear…

Let $k = \mathbb{F}_p$ or $\mathbb{Z}_p$ (or finite extensions of these). Let $G$ be a $p$-valuable group, and form its completed group algebra $kG$. By analysing the conjugation action of $G$ on itself, we prove two structural results.…

Let X be a Hausdorff topological group and G a locally compact subgroup of X. We show that the natural action of G on X is proper in the sense of R. Palais. This is applied to prove that there exists a closed set F of X such that FG=X and…

We characterise those objects in the derived category of a scheme which are a sheaf supported on a closed subscheme in terms of Koszul complexes. This is applied to generalize to arbitrary schemes the fully faithfullness criteria of an…

Let $G(\mathbb{Q})$ be a simply connected Chevalley group over $\mathbb{Q}$ corresponding to a simple Lie algebra $\mathfrak g$ over $\mathbb{C}$. Let $V$ be a finite dimensional faithful highest weight $\mathfrak g$-module and let…

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…

Fix a scheme $X$ over a field of characteristic zero that is equipped with an action of a reductive algebraic group $G$. We give necessary and sufficient conditions for a $G$-equivariant coherent sheaf on $X$ or a bounded-above complex of…

We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on $M \times \bbS^{n_1} \times...\times \bbS^{n_k}$ for some…

We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k[I]$, and the category of extensions of the form $1 \rightarrow \text{Lie}(G, I) \rightarrow E \rightarrow G…

Given an essentially finite type morphism of schemes f: X --> Y and a positive integer d, let f^{d}: X^{d} --> Y denote the natural map from the d-fold fiber product, X^{d}, of X over Y and \pi_i: X^{d} --> X the i'th canonical projection.…

Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and…

Let K be a complete discretely valued field of mixed characteristic (0, p) with possibly imperfect residue field. We prove a Hasse-Arf theorem for the arithmetic ramification filtrations on G_K, except possibly in the absolutely unramified…

Fixed an algebraic scheme $Y$. We suggest a definition for the conjugate of an algebraic scheme $X$ over $Y$ in an evident manner; then $X$ is said to be Galois closed over $Y$ if $X$ has a unique conjugate over $Y$. Now let $X$ and $Y$…

We obtain a sufficient and necessary condition for a finite group to act effectively on a closed flat manifold. Let \ $G=E_{n}(R)$, $EU_{n}(R,\Lambda ),$ $\mathrm{SAut}(F_{n})$ or $\mathrm{SOut}(F_{n}).$ As applications, we prove that when…