Related papers: Stable vectors in Moy-Prasad filtrations

By means of an accurate path-integral Monte Carlo we investigate a two-dimensional ensemble of particles interacting via a Lifshitz-Petrich-Gaussian potential. In particular, analysing structures described by a commensurate ratio between…

We study GIT stability of divisors in products of projective spaces. We first construct a finite set of one-parameter subgroups sufficient to determine the stability of the GIT quotient. In addition, we characterise all maximal orbits of…

In the literature, there are two standard rank filtrations on $K$-theory: an ``unstable'' one which is traditionally defined through the homology of $GL_n$, and a ``stable'' one which was defined by Rognes using the simplicial structure on…

For connected reductive groups G over a finite extension F of Q_p and L the maximal unramified extension of F we study the sets H_{\mu, N}(G) of elements b in G(L) with given Hodge points of (b\sigma), (b\sigma)^2, ..., (b\sigma)^N. We…

We show that if G is a finite constant group acting on a scheme X such that the order of G is invertible in the residue fields of X, then the G-equivariant motivic stable homotopy category of X is equivalent to the stabilization of the…

Let $(\mathcal F_n)_{n\ge 1}$ be a filtration and let $f\ge0$ belong to $L^1(\mathcal F_\infty)$. For the martingale $f_n=\mathbb E[f\mid \mathcal F_n]$ and each $\lambda>0$ we prove a Gundy--Stein decomposition \[ f=g+h+k \] with explicit…

Let $k$ be a field, and let $G$ be a simply connected semisimple k-group which is isotropic and contains a strictly proper parabolic $k$-subgroup $P$. Let $D$ be a discrete valuation ring which is a local ring of a smooth algebraic curve…

Let $\mathcal{O}_K$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ with perfect residue field. We prove the existence of the Hodge-Newton filtration for $p$-divisible groups over $\mathcal{O}_K$ with additional…

We give another proof that a reductive algebraic group is geometrically reductive. We show that a quotient of the semi-stable locus (by a linear action of a reductive algebraic group on a projective scheme) exists, and from this Haboush's…

The building blocks for irreducible smooth representations of p-adic groups are the supercuspidal representations. In these notes that are an expansion of a lecture series given during the IHES summer school 2022 we will explore an explicit…

We define a version of stable maps into the classifying stack $B\mathrm{GL}_N$, and develop a corresponding notion of $K$-theoretic Gromov-Witten invariants. In this setting, the evaluation morphisms are not of finite type; the definition…

Let $G$ be a connected reductive group over $\mathbb{Q}$. In this paper, we will stabilize the local trace formula, in particular, we construct the explicit form of the spectral side of stable local trace formula in the Archimedean case,…

Let $G$ be a reductive group over a nonarchimedean local field $F$. In the quest for a classification of irreducible smooth representations of $G$, it is critical to understand the case of supercuspidal representations -- those whose matrix…

Given a multiparameter filtration of simplicial complexes, we consider the problem of explicitly constructing generators for the multipersistent homology groups with arbitrary PID coefficients. We propose the use of spanning trees as a tool…

Let $p$ be an odd prime and $f \geq 1$. We consider a $p$-adic locally algebraic $\text{GL}_2(\mathbb Q_{p^f})$-representation attached to a tuple of $f$ weights $k=(k_i)$ for $0 \leq i \leq f-1$ and a $p$-adic integer $a_p$ with valuation…

We address a conjecture (referred to as sur in the literature) in the representation theory of a reductive p-adic Lie group G which has important implications for the relationship between mod-p smooth representations and pro-p Iwahori-Hecke…

Motivated by constructing moduli spaces of unstable objects, we use new ideas in non-reductive GIT to construct quotients by parabolic group actions. For moduli problems with semistable moduli spaces constructed by reductive GIT, we…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…

The families of bijective transformations $G_n$ of affine space $K^n$ over general commutative ring $K$ of increasing order with the property of stability will be constructed. Stability means that maximal degree of elements of cyclic…

Let $\mathcal{O}$ be a discrete valuation ring with maximal ideal $\mathfrak{p}$ and with finite residue field $\mathbb{F}_{q}$, the field with $q$ elements where $q$ is a power of a prime $p$. For $r \ge 1$, we write $\mathcal{O}_r$ for…