论文标题
在Leopoldt和Gross的监管图中
On the rank of Leopoldt's and Gross's regulator maps
论文作者
论文摘要
我们将Waldschmidt限制为Leopoldt的缺陷，并证明Gross的缺陷是数字字段的任意扩展的类似界限。作为一种应用，我们证明了Gross的有限猜想（也称为Gross-Kuz'min猜想）的新案例，但我们表明，Gross的$ P $ -ADIC调节器至少具有猜想等级的一半。我们还描述并计算了总缺陷的非周期性类似物。
We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of Gross's finiteness conjecture (also known as the Gross-Kuz'min conjecture) beyond the classical abelian case, and we show that Gross's $p$-adic regulator has at least half of the conjectured rank. We also describe and compute non-cyclotomic analogues of Gross's defect.
