论文标题
P-Adic随机典型代数是一个未受到的磁场的可能性
The probability that a p-adic random étale algebra is an unramified field
论文作者
论文摘要
我们研究由I.I.D的随机多项式产生的随机典型代数。根据$ \ mathbb {z} _p $在HAAR测量中分配的系数。我们确定该随机代数是明确的磁场的概率。此外，我们证明了由Bhargava，Cremona，Fisher和Gajović做出的私人案例。更确切地说，我们表明，这种概率是$ p $的合理函数，在将$ P $替换为$ 1/p $的情况下是不变的。
We study the random étale algebra generated by a random polynomial with i.i.d. coefficients distributed according to Haar measure normalized on $\mathbb{Z}_p$. We determine the probability that this random algebra is an unramified field, explicitly. In addition, we prove a private case of a conjecture made by Bhargava, Cremona, Fisher, and Gajović. More precisely, we show that this probability is a rational function of $p$ that is invariant under replacing $p$ by $1/p$.
