Related papers: On the crystalline period map

In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.

In 1989, Faltings proved the comparison theorem between \'etale cohomology and crystalline cohomology by studying Fontaine-Faltings modules and crystalline representations. In his paper, he mentioned these modules and representations can be…

We define, prove the existence and obtain explicit expressions for classical time delay defined in terms of sojourn times for abstract scattering pairs (H_0,H) on a symplectic manifold. As a by-product, we establish a classical version of…

In this short note, we prove a purity result for crystalline local systems on a smooth $p$-adic affine formal scheme. Our method is based on the prismatic description of crystalline local systems.

This is an exposition of work on Artin's Conjecture on the zeros of $p$-adic forms. A variety of lines of attack are described, going back to 1945. However there is particular emphasis on recent developments concerning quartic forms on the…

Fontaine-Mazur Conjecture is one of the core statements in modern arithmetic geometry. Several formulations were given since its original statement in 1993, and various angles have been adopted by numerous authors to try to tackle it.…

In this paper, we prove a conjecture of Schnell in the surface case.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

Let $A/\mathbb{Q}$ be a Jacobian variety and let $F$ be a totally real, tamely ramified, abelian number field. Given a character $\psi$ of $F/\mathbb{Q}$, Deligne's Period Conjecture asserts the algebraicity of the suitably normalised value…

We prove Haynes' version of the Duffin--Schaeffer conjecture for the $p$-adic numbers. In addition, we prove several results about an associated related but false conjecture, related to $p$-adic approximation in the spirit of Jarn\'ik and…

Berthelot's conjecture predicts that under a proper and smooth morphism of schemes in characteristic $p$, the higher direct images of an overconvergent $F$-isocrystal are overconvergent $F$-isocrystals. In this paper we prove that this is…

Building on work of Crew, we give a rigid cohomological analogue of the main result of Deligne's "Weil II"; this makes it possible to give a purely p-adic proof of the Weil conjectures. Ingredients include a p-adic analogue of Laumon's…

As an example of relative p-adic Hodge theory, we sketch the construction of the universal admissible filtration of an isocrystal (\phi$-module) over the completion of the maximal unramified extension of Q_p, together with the associated…

In the paper a theorem of Piccard's type is proved and, consequently, the continuity of $\mathcal{D}$-measurable polynomial functions of $n$-th order as well as $\mathcal{D}$-measurable $n$-convex functions is shown. The paper refers to the…

For the class of non-degenerate box splines, we prove that these box splines are piecewise polynomial. This is not a new result, it is in fact a well known and useful property of box splines. However, our proof is constructive, and the main…

We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning conic sections.

I report the results of a series of works on the phase diagram of theories with a different number of colors and/or quarks in a different representation than in QCD. Similarities as well as differences as compared to the real world are…

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

This note serves to provide additional details for the proof of Lemma 3.6 in our paper [Liu, Zhang and Zhang, Comm. Math. Sci., 3(2005), pp.201-218]. Moreover, we will also present an alternative, yet simpler, proof based on arguments in…

In this note, we study the infinitesimal forms of Deligne cycle class maps. As an application, we prove that the infinitesimal form of a conjecture by Beilinson is true.