Related papers: Congruence kernels around affine curves

We show that for a sufficiently simple surface $S$, a right-angled Artin group $A(\Gamma)$ embeds into $\Mod(S)$ if and only if $\Gamma$ embeds into the curve graph $\mC(S)$ as an induced subgraph. When $S$ is sufficiently complicated,…

In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for…

It is known that by using the commutator operation, for each congruence modular algebra $A$ one can define a notion of prime congruence. The set $Spec(A)$ of prime congruences of $A$ is endowed with a Zariski style topology. The…

Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus $g$ with one boundary component, that are double coverings of…

We study the generalized Hodge conjecture for certain sub-Hodge structure defined as the kernel of the cup product map with a big cohomology class, which is of Hodge coniveau at least 1. As predicted by the generalized Hodge conjecture, we…

Questions related to Brauer-Manin obstructions to the Hasse principle and weak approximation for homogeneous spaces of tori over a number field are well-studied, generally using arithmetic duality theorems, starting with works of Sansuc and…

We study the properties of the fundamental group of an affine curve over an algebraically closed field of characteristic $p$, from the point of view of embedding problems. In characteristic zero, the fundamental group is free, but in…

We present explicit models for Shimura curves X_D and Atkin-Lehner quotients X_D/w_m of them of genus 2. We show that several equations conjectured by Kurihara are correct and compute for them the kernel of Ribet's isogeny J_0(D)^{new} -->…

In this paper we characterize the monoid congruences of commutative semigroups by the help of the notion of the separator of subsets of semigroups. We show that every monoid congruence of a commutative semigroup S can be constructed by the…

In [31,32,33] the Gauss-Bonnet formulas for coherent tangent bundles over compact oriented surfaces (without boundary) were proved. We establish the Gauss-Bonnet theorem for coherent tangent bundles over compact oriented surfaces with…

We define the affine stratification number asn X of a scheme X. For X equidimensional, it is the minimal number k such that there is a stratification of X by locally closed affine subschemes of codimension at most k. We show that the affine…

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…

Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…

We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain a complete characterization of congruence-simpleness for Steinberg algebras of second-countable ample groupoids,…

Let $C \s \pr^2$ be an irreducible plane curve whose dual $C^* \s \pr^{2*}$ is an immersed curve which is neither a conic nor a nodal cubic. The main result states that the Poincar\'e group $\pi_1(\pr^2 \se C)$ contains a free group with…

The geometry of a graph $G$ embedded on a closed oriented surface $S$ can be probed by counting the intersections of $G$ with closed curves on $S$. Of special interest is the map $c \mapsto \mu_G(c)$ counting the minimum number of…

Let $E$ be an $1$-Ahlfors regular subset of the Heisenberg group $\mathbb{H}$. We prove that there exists a $-1$-homogeneous kernel $K_1$ such that if $E$ is contained in a $1$-regular curve the corresponding singular integral is bounded in…

We consider the Birman-Hilden inclusion $\varphi\colon\mathfrak{Br}_{2g+1}\to\Gamma_{g,1}$ of the braid group into the mapping class group of an orientable surface with boundary, and prove that $\varphi$ is stably trivial in homology with…

In this paper, we introduce an algebro-geometric formulation for Siegel's theorem using an improvement of Lang's version of Roth's theorem over finitely generated fields of characteristic zero. In fact, we prove that, for an affine open…

We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character variety of a finitely generated and presented group. We give…