相关论文: Stacks of ramified abelian covers

Let G be a complex reductive algebraic group (not necessarily connected), let K be a maximal compact subgroup, and let A be a finitely generated Abelian group. We prove that the conjugation orbit space Hom(A,K)/K is a strong deformation…

We show some of the conjectures of Pappas and Rapoport concerning the moduli stack of $\mathcal{G}$-torsors on a curve C, where $\mathcal{G}$ is a semisimple Bruhat-Tits group scheme on C. In particular we prove the analog of the…

Using the Katz-Arinkin algorithm we give a classification of irreducible rigid irregular connections on a punctured $\mathbb{P}^1_{\mathbb{C}}$ having differential Galois group $G_2$, the exceptional simple algebraic group, and slopes…

Let $$1 \to H \to G \to Q \to 1$$ be an exact sequence where $H= \pi_1(S)$ is the fundamental group of a closed surface $S$ of genus greater than one, $G$ is hyperbolic and $Q$ is finitely generated free. The aim of this paper is to provide…

Within the Schottky problem, the study of special subvarieties of the Torelli locus has long been of great interest. We describe a representation-theoretic criterion for a Jacobian variety arising from a $G$-Galois cover of $\mathbb{P}^1$…

Let $f: X \to Y$ be a regular covering of a surface $Y$ of finite type with nonempty boundary, with finitely-generated (possibly infinite) deck group $G$. We give necessary and sufficient conditions for an integral homology class on $X$ to…

Let G be a finite group. To every smooth G-action on a compact, connected and oriented surface we can associate its data of singular orbits. The set of such data becomes an Abelian group B_G under the G-equivariant connected sum. We will…

Let $G$ be a connected reductive complex algebraic group, and $E$ a complex elliptic curve. Let $G_E$ denote the connected component of the trivial bundle in the stack of semistable $G$-bundles on $E$. We introduce a complex analytic…

Given a $G$-Galois branched cover of the projective line over a number field $K$, we study whether there exists a closed point of $\mathbb{P}^1_K$ with a connected fiber such that the $G$-Galois field extension induced by specialization…

Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…

Given a connected smooth projective surface X over the complex numbers, together with a simple normal crossings divisor D on it, we study finite normal covers Y of X that are unramified outside D. Given moreover a fibration of X onto a…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

Let $X$ be a smooth, projective, geometrically connected curve over a finite field $\mathbb{F}_q$, and let $G$ be a split semisimple algebraic group over $\mathbb{F}_q$. Its dual group $\hat{G}$ is a split reductive group over $\mathbb{Z}$.…

According to Markov, a subset of an abelian group G of the form {x in G: nx=a}, for some integer n and some element a of G, is an elementary algebraic set; finite unions of elementary algebraic sets are called algebraic sets. We prove that…

In this article, we give a proof for a geometric presentation theorem for any irreducible scheme $X$ smooth projective over a discrete valuation ring $R$. As a consequence, for any reductive $R$-group scheme $\mathbf{G}$, we prove that any…

For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduce to the moduli space of stable curves and a…

Given a Galois cover of curves $f$ over a field of characteristic $p$, the lifting problem asks whether there exists a Galois cover over a complete mixed characteristic discrete valuation ring whose reduction is $f$. In this paper, we…

Let $G$ be a split reductive group with $\dim Z(G) \leq 1$. We show that for any prime $p$ that is large enough relative to $G$, there is a finitely ramified Galois representation $\rho \colon \Gamma_{\mathbb Q} \to G(\mathbb Z_p)$ with…

Let $X$ be a reduced connected $k$-scheme pointed at a rational point $x \in X(k)$. By using tannakian techniques we construct the Galois closure of an essentially finite $k$-morphism $f:Y\to X$ satisfying the condition…

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. To any irreducible smooth…