Related papers: On the Breuil-Schneider conjecture: Generic case

In this short survey, we explain Parshin's proof of the geometric Bombieri-Lang conjecture, and show that it can be used to give an alternative proof of Xie-Yuan's recent resolution of the geometric Bombieri-Lang conjecture for projective…

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N\in \N$ and for {\it number fields}. The main new observation is a modification of a theorem due to Glenn Stevens for the…

First, we shall formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms…

In this paper we prove an estimate for the total variation distance, in the framework of the Breuer-Major theorem, using the Malliavin-Stein method, assuming the underlying function $g$ to be once weakly differentiable with $g$ and $g'$…

We give in the present work a new methodology that allows to give isoperimetric proofs, for Kneser's Theorem and Kemperman's structure Theory and most sophisticated results of this type. As an illustration we present a new proof of Kneser's…

We produce Brill-Noether general graphs in every genus, confirming a conjecture of Baker and giving a new proof of the Brill-Noether Theorem, due to Griffiths and Harris, over any algebraically closed field.

This paper generalizes Shelah's generic pair conjecture (now theorem) for the measurable cardinal case from first order theories to finite diagrams. We use homogeneous models in the place of saturated models.

We discuss two approaches to producing generalized parity proofs of the Kochen-Specker theorem. Such proofs use contexts of observables whose product is $I$ or $-I$; we call them constraints. In the first approach, one starts with a fixed…

Using geometric methods we prove the standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a finite field.

We use the Taylor-Wiles-Kisin patching method to investigate the multiplicities with which Hecke eigensystems appear in the mod-$\ell$ cohomology of unitary Shimura sets, associated to central simple algebras of the form $B=M_2(D)$, for $D$…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

An technically interesting proof of a known theorem.

We prove a few simple cases of a random graph statement that would imply the "second" Kahn--Kalai Conjecture. Even these cases turn out to be reasonably challenging, and it is hoped that the ideas introduced here may lead to further…

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

We prove a conjecture of Klopsch-Voll on the signed generating function of a new statistic on the quotients of the symmetric groups. As a consequence of our results we also prove a conjecture of Stasinski-Voll in type $B$.

We prove Breuil's lattice conjecture for higher Hodge-Tate weights in the case of $\mathrm{GL}_2(K)$ where $K$ is an unramified extension of $\mathbb{Q}_p$. More precisely, under some genericity conditions, we show that the lattice inside a…

Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…

We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.

New cases of the multiplicity conjecture are considered.

The classical Brauer-Siegel conjecture describes the asymptotic behaviour of the product of the class number and the regulator in families of number fields. All known cases of the conjecture rely on reducing the problem, via group theoretic…