论文标题
计数原始晶格的标志
Counting flags of primitive lattices
论文作者
论文摘要
我们计算原始晶格的标志，这些标志是$ {0} =λ^{（0）}<λ^{（1）} <\ cdots <λ^{（（\ ell）} = \ mathbb {z}^n $，每个$λ^{（i）是$ nis primitive n $ n $ {计数是关于两个不同自然的高度函数的，这使我们能够为旗帜品种而不是理性数字提供新的猜想。我们推断出标志品种中有理点的等分，以及连续商的形状的等分分配，$λ^{（i）}/λ^{（i-1）} $。在此过程中，我们概括了施密特（Schmidt）以及我们自己的先前工作，以计算排名$ d <n $的原始晶格。
We count flags of primitive lattices, which are objects of the form ${0}=Λ^{(0)}<Λ^{(1)}< \cdots <Λ^{(\ell)}= \mathbb{Z}^n$, where every $Λ^{(i)}$ is a primitive lattice in $\mathbb{Z}^n$. The counting is with respect to two different natural height functions, allowing us to give a new proof of the Manin conjecture for flag varieties over rational numbers. We deduce the equidistribution of rational points in flag varieties, as well as the equidistribution of the shapes of the successive quotient lattices, $Λ^{(i)}/Λ^{(i-1)}$. In doing so, we generalize previous work of Schmidt, as well as our own, on counting primitive lattices of rank $d<n$.
