The sequence of prime numbers p for which a variety over ℚ has no p-adic point plays a fundamental role in arithmetic geometry. This sequence is deterministic, however, we prove that if we choose a typical variety from a family then the sequence has random behaviour. We furthermore prove that this behaviour is modelled by a random walk in Brownian motion. This has several consequences, one of them being the description of the finer properties of the distribution of the primes in this sequence via the Feynman–Kac formula.

中文翻译：

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阻碍有理点存在的素数的大小

素数序列p超过 ℚ 的变体没有p-adic 点在算术几何中起着基本作用。这个序列是确定性的，然而，我们证明如果我们从一个家族中选择一个典型的品种，那么这个序列具有随机行为。我们进一步证明了这种行为是通过布朗运动中的随机游走来建模的。这有几个结果，其中之一是通过 Feynman-Kac 公式描述了该序列中素数分布的更精细性质。