Apéry constants of homogeneous varieties

某些齐性空间族的势密度

Potential density for some families of homogeneous spaces

对于定义在数域上的光滑的、射影的齐次簇族，我们证明了如果势密度对基的有理点成立，那么它对全空间也成立。Campana和Peternell的一个猜想，已知维数最多为4，并且对于某些高维情形，则意味着切丛为nef的数域上光滑射影簇的有理点的势密度。

齐次簇上的丢番图逼近指数

Diophantine approximation exponents on homogeneous varieties

近年来，在丢番图逼近和齐次动力学的界面上取得了非常重要的进展。在本文的第一部分中，我们给出了一个简短的阐述字典开发的Dani和Kleinbock-Margulis的关系丢番图性质的向量分布的轨道流的空间上的幺模格。在本文的第二部分中，我们简要地描述了作者最近开发的这本字典的扩展，它建立了一个类似的动力学对应一般格轨道上的齐性空间。我们专注于具体的问题估计指数的丢番图逼近算术格作用于代数簇。在第三部分中，我们通过在一些基本情况下建立稠格轨道的丢番图指数的显式界，来证明我们的结果。其中包括对仿射空间的线性作用和仿射作用，以及对固定行列式矩阵簇的作用。在某些情况下，这些指数被证明是最好的可能。

Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant

We show that if a rational map is constant on each isomorphism class of unpolarized abelian varieties of a given dimension, then it is a constant map. Our results are motivated by and shed light on a proposed construction of a cryptographic protocol for multiparty non-interactive key exchange.

Linnik's problem in fiber bundles over quadratic homogeneous varieties

We compute the statistics of $SL_{d}(\mathbb{Z})$ matrices lying on level sets of an integral polynomial defined on $SL_{d}(\mathbb{R})$, a result that is a variant of the well known theorem proved by Linnik about the equidistribution of radially projected integral vectors from a large sphere into the unit sphere. Using the above result we generalize the work of Aka, Einsiedler and Shapira in various directions. For example, we compute the joint distribution of the residue classes modulo $q$ and the properly normalized orthogonal lattices of primitive integral vectors lying on the level set $-…

Counting integral points on some homogeneous varieties with large reductive stabilizers

Let G be a semisimple group over rational numbers and H is a subgroup over rational numbers. Given a representation of G and an integral vector x whose stabilizer is equal to H. In this paper we investigate the asymptotic of integral points on Gx with bounded height. We find its asymptotic up to an implicit constant when H is large in G but we allow the presence of intermediate subgroups. This is achieved by a novel combination of two equidistribution results in two different settings: one is that of Eskin, Mozes and Shah on a Lie group modulo a lattice and the other one is a result of Chamber…

关于函数域上常数普通阿贝尔簇的Iwasawa Main猜想

The Iwasawa Main conjecture of constant ordinary abelian varieties over function fields

本文研究了$\ZZ_p^d$上的常数普通阿贝尔簇的岩泽主猜想的一个几何模拟--函数域在有限集上分歧的扩张.

广义Hermite常数、Voronoi理论和旗簇的高度

Generalised Hermite Constants, Voronoi Theory and Heights on Flag Varieties

本文研究了T。渡边为此，一个高度，这自然适用于旗品种，是建立和概念的完美和eutaxy特征的极值。最后，我们熟悉了一些关系式（如Korkine-Zolotareff约化），上界和与这些常数有关的计算。