Related papers: An observation concerning highly ramified $\epsilo…

We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown--York quasi-local mass as it possesses positivity and rigidity properties, and therefore the stability of this rigidity statement can be…

Let $F$ be a non-archimedean local field of characteristic different from $2$ and $G$ be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse…

This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…

This paper is concerned with extensions of geometric stability theory to some nonelementary classes. We prove the following theorem: Theorem: Let C be a large homogeneous model of a stable diagram D. Let p, q in S_D(A), where p is…

In this work we prove that the local $\gamma$-factor arising from the doubling integrals for split general spin groups is stable. This deep property of the $\gamma$-factor constitutes an important ingredient in the application of the…

In this paper, we consider compact graphical manifolds with boundary over (locally) hyperbolic static space. We prove the stability of the positive mass theorem with respect to the Federer--Fleming flat distance for the static quasi-local…

Let $p$ be a rational prime, let $F$ denote a finite, unramified extension of $\mathbb{Q}_p$, let $K$ be the completion of the maximal unramified extension of $\mathbb{Q}_p$, and let $\overline{K}$ be some fixed algebraic closure of $K$.…

Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the sequence of p-adic groups $\{GL_n(F)\}_{n=0}^\infty$, with multiplication defined through parabolic induction. We study the problem of the…

In the local, characteristic 0, non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies that an…

We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called…

Let $\mathcal{F}$ be written as $ f^{*}(\mathcal{G})$, where $\mathcal{G}$ is a $1$-dimensional foliation on $ {\mathbb P^{n-1}}$ and $f:{\mathbb P^n}--->{\mathbb P^{n-1}}$ a non-linear generic rational map. We use local stability results…

This is the last version of AG/0111277. Here the old abstract: We define $\epsilon$-factors in the de Rham setting and calculate the determinant of the Gau\ss-Manin connection for a family of (affine) curves and a vector bundle equipped…

We study inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold under dimensional reduction. Stability due to different types of effective potentials is analyzed for specific configurations of…

Let E/F be a CM field split above a finite place v of F, let l be a rational prime number which is prime to v, and let S be the set of places of E dividing lv. If E_S denotes a maximal algebraic extension of E unramified outside S, and if u…

Let $F$ be a totally real field in which $p$ is unramified. Let $\overline{r}: G_F \rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a modular Galois representation which satisfies the Taylor--Wiles hypotheses and is tamely ramified…

A strongly polynomial sequence of graphs $(G_n)$ is a sequence $(G_n)_{n\in\mathbb{N}}$ of finite graphs such that, for every graph $F$, the number of homomorphisms from $F$ to $G_n$ is a fixed polynomial function of $n$ (depending on $F$).…

We show that almost all (Bushnell and Kutzko) types of PGL(2,F), F a non-Archimedean locally compact field of odd residue characteristic, naturally appear in the cohomology of finite graphs.

Let $\Gamma$ be an irreducible lattice in a semisimple Lie group of real rank at least $2$. Suppose that $\Gamma$ has property (T;FD), that is, its finite dimensional representations have a uniform spectral gap. We show that if $\Gamma$ is…

We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for $GL_n(k)$. Let $k$ be an algebraically closed field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$ with…

We consider two families X_n of varieties on which the symmetric group S_n acts: the configuration space of n points in C and the space of n linearly independent lines in C^n. Given an irreducible S_n-representation V, one can ask how the…