Related papers: Stable vectors in Moy-Prasad filtrations

Let K be a maximal unramified extension of a nonarchimedean local field with arbitrary residual characteristic p. Let G be a reductive group over K which splits over a tamely ramified extension of K. We show that the associated Moy-Prasad…

Let G be a reductive group over a non-archimedean local field k. We provide necessary conditions and sufficient conditions for all tori of G to split over a tamely ramified extension of k. We then show the existence of good semisimple…

In 2014, Reeder and Yu constructed epipelagic representations of a reductive $p$-adic group $G$ from stable functions on shallowest Moy-Prasad quotients. In this paper, we extend these methods when $G$ is split. In particular, we classify…

This paper gives a classification of stable vectors in dual Vinberg representations coming from a graded Lie algebra of type $F_4$ in a way that is independent of the field of definition. Relating these gradings to Moy-Prasad filtrations,…

For an essentially tame supercuspidal representation $\pi$ of a connected reductive $p$-adic group $G$, we establish two distinct and complementary sufficient conditions for the irreducible components of its restriction to a maximal compact…

Suppose $G$ is a tamely ramified $p$-adic reductive group. We construct a partial local Langlands correspondence between the set of irreducible smooth representations of $G$ having depth $r$ and a certain set of $G^\vee$-conjugacy classes…

Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we…

Let G be a reductive group over an algebraically closed field k. Consider the moduli space of stable principal G-bundles on a smooth projective curve C over k. We give necessary and sufficient conditions for the existence of Poincar\'e…

Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\mathbf{G}$ is a connected reductive $k$-group. If $\mathbf{T}$ is a $K$-minisotropic maximal $k$-torus in $\mathbf{G}$, then we use…

The Bruhat-Tits theory is a key ingredient in the construction of irreducible smooth representations of $p$-adic reductive groups. We describe generalizations to arbitrary such representations of several results recently obtained in the…

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it…

We extend (scheme-theoretic) Bruhat-Tits theory to quasi-reductive groups i.e. with trivial split unipotent radical over discretely valued henselian non-archimedean fields $K$, whose ring of integers is excellent and residue field is…

Let $k$ denote a field with nontrivial discrete valuation. We assume that $k$ is complete with perfect residue field. Let $G$ be the group of $k$-rational points of a reductive, linear algebraic group defined over $k$. Let $\gg$ denote the…

We propose a new approach to constructing semistable integral models of hypersurfaces over a discretely valued complete field K. For each stable hypersurface X over K we define a continuous stability function on the Bruhat-Tits building of…

Let $G$ be a reductive algebraic group over an algebraically closed field and let $V$ be a quasi-projective $G$-variety. We prove that the set of points $v\in V$ such that ${\rm dim}(G_v)$ is minimal and $G_v$ is reductive is open. We also…

Let $p$ be an odd prime number, $K_{f}$ the finite unramified extension of $\mathbb{Q}_{p}$ of degree $f$, and $G_{K_{f}}$ its absolute Galois group. We construct analytic families of \'etale $(\varphi,\Gamma)$-modules which give rise to…

In this work, we present explicit constructions and computations of representative cycles for a nontrivial 2-parameter persistence module arising from the configuration space of metric star graphs. For all edge-length vector…

We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non-Reductive GIT. Our quotients come with explicit projective…

Let $K$ be a number field, and let $G\subset K^\times$ be a finitely generated subgroup. Fix some prime number $\ell$, and consider the set of primes $\mathfrak{p}$ of $K$ satisfying the following property: the reduction of $G$ modulo…

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point…