Related papers: $p$-adic estimates for multiplicative character su…

We discuss recent developments in $p$-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for "compact $p$-adic manifolds" over new period maps on moduli spaces of abelian…

We obtain new bounds of exponential sums modulo a prime $p$ with sparse polynomials $a_0x^{n_0} + \cdots + a_{\nu}x^{n_\nu}$. The bounds depend on various greatest common divisors of exponents $n_0, \ldots, n_\nu$ and their differences. In…

We prove $p$-adic versions of a classical result in arithmetic geometry stating that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of…

We show that the special values at tuples of positive integers of the $p$-adic multiple $L$-function introduced by the first-named author et al. can be expressed in terms of the cyclotomic multiple harmonic values introduced by the…

We prove the remaining part of the conjecture by Denef and Sperber [Denef, J. and Sperber, S., \textit{Exponential sums mod $p^n$ and {N}ewton polyhedra}, Bull. Belg. Math. Soc., {\bf{suppl.}} (2001) 55-63] on nondegenerate local…

We prove the intersection of Igusa's Conjecture of [Igusa, J., "Lectures on forms of higher degree", Lect. math. phys., Springer-Verlag, 59 (1978)] and the Denef - Sperber Conjecture of [Denef, J. and Sperber, S., "Exponential sums mod p^n…

We prove that the density of polynomials $P(x)=\sum_{i=0}^n a_n x^n$ over a local field $K$ generating an \'etale extension with specified splitting type is a rational function in terms of the size of the residue field of $K$ in the case…

We show that, for a polarised smooth projective variety $B \hookrightarrow \mathbb{P}^n_k$ of dimension $\geq 2$ over an infinite field $k$ and an abelian variety $A$ over the function field of $B$, there exists a dense Zariski open set of…

We generalize results on the $p$-adic valuations of $S(n,k)$, the Stirling number of the second kind and $s(n,k)$ the Stirling number of the first kind. We have several new estimates for these valuations, along with criteria for when the…

In this paper, we analyze the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are…

Let p be a prime number and f an overconvergent p-adic automorphic form on a definite unitary group which is split at p. Assume that f is of "classical weight" and that its Galois representation is crystalline at places dividing p, then f…

$T$-adic exponential sums associated to a Laurent polynomial $f$ are introduced. They interpolate all classical $p^m$-power order exponential sums associated to $f$. The Hodge bound for the Newton polygon of $L$-functions of $T$-adic…

We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field $k=\Fq$ for two classes of polynomials which are invariant under a large…

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

Let $X$ be a smooth complex projective variety. A recent conjecture of S. Kov\'acs states that if t\ he $p^{\text{th}}$-exterior power of the tangent bundle $T_X$ contains the $p^{\text{th}}$-exterior power of an ample vector bundle, then…

The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that i) implies ii) in characteristic 0, using…

We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by…

We reinterpret a result of Pop and Stix on the $p$-adic section conjecture in terms of Berkovich spaces and fixed points. In doing this, we see a version of the result extends to larger classes of fields, which in turn allows us to prove a…

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the estimates of the proximity of sequential…

We prove the weight-monodromy conjecture for varieties which are p-adically uniformized by a product of the Drinfeld upper half spaces. It is an easy consequence of Dat's work on the cohomology complex of the Drinfeld upper half space.