相关论文: Chabauty Limits of Subgroups of $SL(n, \mathbb{Q}_…

In this paper we describe the local limits under conjugation of all closed connected subgroups of $SL_3(\mathbb{R})$ in the Chabauty topology.

We classify Chabauty limits of groups fixed by various (abstract) involutions over $SL(2,F)$, where $F$ is a finite field-extension of $\mathbb{Q}_p$, with $p\neq 2$. To do so, we first classify abstract involutions over $SL(2,F)$ with $F$…

Let $\mathcal{C}(G)$ denote the Chabauty space of closed subgroups of the locally compact group $G$. In this paper, we first prove that $\mathcal{C} (\mathbb{Q}_p^\times)$ is a proper compactification of $\mathbb{N}$, identified with the…

Let GF denote the rational points of a semisimple group G over a non-archimedean local field F, with Bruhat-Tits building X. This paper contains five main results. We prove a convergence theorem for sequences of parahoric subgroups of GF in…

Let G be a real semisimple Lie group with finite center, with a finite number of connected components and without compact factor. We are interested in the homogeneous space of Cartan subgroups of G, which can be also seen as the space of…

The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. Let X be a symmetric space of noncompact type, and G be its group of isometries. The space X identifies…

A limit group is the limit of a sequence of conjugates of the diagonal Cartan subgroup, C, of SL(3,R). We show C has 5 possible limit groups, up to conjugacy. Each limit group is determined by an equivalence class of nonstandard triangle,…

Given a locally finite leafless tree $ T $, various algebraic groups over local fields might appear as closed subgroups of $ \text{Aut} (T)$. We show that the set of closed cocompact subgroups of $ \text{Aut} (T)$ that are isomorphic to a…

We study Chabauty limits of the fixed-point group of $k$-points $H_k$ associated with an involutive $k$-automorphism $\theta$ of a connected linear reductive group $G$ defined over a non-Archimedean local field $k$ of characteristic zero.…

We give a quadratic lower bound on the dimension of the space of conjugacy classes of subgroups of SL(n,R) that are limits under conjugacy of the diagonal subgroup. We give the first explicit examples of abelian n-1 dimensional subgroups of…

We study conjugacy limits of certain of subgroups inside $\SL(2,\R)\ltimes\R^2$. These subgroups have a common feature that any two in the same category are conjugates of each other.

Let $T$ be a locally finite tree without vertices of degree $1$. We show that among the closed subgroups of $\mathrm{Aut}(T)$ acting with a bounded number of orbits, the Chabauty-closure of the set of topologically simple groups is the set…

We give a complete description of the closure of the space of one-generator closed subgroups of PSL2(R) for the Chabauty topology, by computing explicitly the matrices associated with elements of Aut(D) = PSL2(R), and finding quantities…

Given a smooth, proper, geometrically integral curve $X$ of genus $g$ with Jacobian $J$ over a number field $K$, Chabauty's method is a $p$-adic technique to bound $\# X(K)$ when $\mathrm{rank}\ J(K) < g$. We study limitations of a variant…

The Chabauty space of a topological group is the set of its closed subgroups, endowed with a natural topology. As soon as $n>2$, the Chabauty space of $R^n$ has a rather intricate topology and is not a manifold. By an investigation of its…

We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions associated to representations of finite…

We study the freeness problem for subgroups of $\operatorname{SL}_2(\mathbb{C})$ generated by two parabolic matrices. For $q = r/p \in \mathbb{Q} \cap (0,4)$, where $p$ is prime and $\gcd(r,p)=1$, we initiate the study of the algebraic…

Let $\mathcal{C}$ be a smooth, projective, geometrically integral curve defined over a perfect field $\mathbb{F}$. Let $k=\mathbb{F}(\mathcal{C})$ be the function field of $\mathcal{C}$. Let $\mathbf{G}$ be a split simply connected…

Given a quasi-reductive group $G$ over a local field $k$, using Berkovich geometry, we exhibit a family of $G(k)$-equivariant compactifications of the Bruhat-Tits building $\mathcal B(G, k)$, constructed and investigated by Solleveld and…

When equipped with the natural topology first defined by Chabauty, the closed subgroups of a locally compact group $G$ form a compact space $\Cal C(G)$. We analyse the structure of $\Cal C(G)$ for some low-dimensional Lie groups,…