Related papers: On the Unipotent $p$-adic Simpson Correspondence

Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence whose construction has been taken up by various authors, according to several approaches. Following the one we initiated previously, we develop in this new…

We generalise a theorem on the existence of Frobenius isocrystal and Fontaine-Laffaille module structures on rigid flat connections to the non-proper setting. The proof is based on a new strategy of a point-set topological flavour, which…

The aim of this work is to establish congruences $\left( \operatorname{mod}p^{2}\right) $ involving the trinomial coefficients $\binom{np-1}{p-1}_{2}$ and $\binom{np-1}{\left( p-1\right)/2}_{2}$ arising from the expansion of the powers of…

In earlier papers (A. N. Kochubei, Pacif. J. Math., 269 (2014), 355-369; J. Math. Anal. Appl.483 (2020), Article 123609), one of the authors developed a theory of pseudo-differential equations for radial real-valued functions on a…

We start with a curve over an algebraically closed ground field of positive characteristic $p>0$. By using specialization techniques, under suitable natural coprimality conditions, we prove a cohomological Simpson Correspondence between the…

We study differential $p$-forms on non-smooth and possibly fractal metric measure spaces, endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the localization of antisymmetric functions of $p+1$…

In this paper we study $p$-adic Diophantine approximation on manifolds, specifically multiplicative Diophantine approximation on affine subspaces and a Diophantine dichotomy for analytic $p$-adic manifolds.

Wavelet analysis has been extended to the $p$-adic line $\mathbb{Q}_p$. The $p$-adic wavelets are complex valued functions with compact support. As in the case of real wavelets, the construction of the basis functions is recursive,…

We give an explicit finite-dimensional model for the derived moduli stack of flat connections on $\mathbb{C}^k$ with logarithmic singularities along a weighted homogeneous Saito free divisor. We investigate in detail the case of plane…

Let $p$ be a prime number. The $p$-power cyclic resultant of a polynomial is the determinant of the Sylvester matrix of $t^{p^n}-1$ and the polynomial. It is known that the sequence of $p$-power cyclic resultants and its non-$p$-parts…

This thesis studies normal forms for Poisson structures around symplectic leaves using several techniques: geometric, formal and analytic ones. One of the main results (Theorem 2) is a normal form theorem in Poisson geometry, which is the…

According to Laumon, an affine Springer fiber is homeomorphic to the universal abelian covering of the compactified Jacobian of a spectral curve. We construct equivariant deformations $f_{n}:\overline{\mathcal{P}}_{n}\to \mathcal{B}_{n}$ of…

The object of this paper is to study relationship between successive coefficients of some subclasses of the class of univalent functions in the unit disk. the result obtained is sharp, and is used to provide a new, short proof of the…

First we explain the concept of local deformation over a 'parameter' algebra P, in particular the notion of a P-lattice in a Lie group. Purpose of this article is to define the spaces of automorphic resp. cusp forms on the upper half plane…

It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…

In this article, we consider the estimation of exponential sums along the points of the reduction mod $p^{m}$ of a $p$-adic analytic submanifold of $ \mathbb{Z}_{p}^{n}$. More precisely, we extend Igusa's stationary phase method to this…

Poincar\'e series of $p$-adic, definable equivalence relations have been studied in various cases since Igusa's and Denef's work related to counting solutions of polynomial equations modulo $p^n$ for prime $p$. General semi-algebraic…

We introduce strong p-completeness and use them for studying the continuous dependence of solutions of SDE's on non-compact manifolds. We obtain conditions for the existence of global smooth solution flow, and prove their diffeomorphism…

We consider local densities for $p$-adic quaternion hermitian forms (hermitian forms over a division quaternion algebra over a ${\mathfrak p}$-adic field $k$). The author has studied such forms in connection with spherical functions on the…

This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we…