论文标题
预期价值的本地至全球原则
Local to global principle for expected values
论文作者
论文摘要
本文构建了一个新的本地和全局原理，用于自由$ \ mathbb {z} $ - 有限等级的模块。在我们的策略中，我们使用与埃克德哈尔（Ekedhal）的筛子相同的哲学，后来在其本地至全球密度原理中扩展和改进。我们表明，在原则上使用的$ p $ -ADIC子集系统上的一些其他假设下，当人们必须计算预期值（不仅是密度）时，也可以使用$ p $ - 亚种的措施。此外，我们证明了我们的其他假设是鲜明的，从某种意义上说，当其中任何一个都缺失时，存在明确的反例。特别是，当人们对预期价值而不是密度感兴趣时，不保证在Poonen和Stoll原理中起作用的$ p $ -ADIC子集的系统。最后，我们提供了该方法的新应用，也提供了即时证明已知结果。
This paper constructs a new local to global principle for expected values over free $\mathbb{Z}$-modules of finite rank. In our strategy we use the same philosophy as Ekedhal's Sieve for densities, later extended and improved by Poonen and Stoll in their local to global principle for densities. We show that under some additional hypothesis on the system of $p$-adic subsets used in the principle, one can use $p$-adic measures also when one has to compute expected values (and not only densities). Moreover, we show that our additional hypotheses are sharp, in the sense that explicit counterexamples exist when any of them is missing. In particular, a system of $p$-adic subsets that works in the Poonen and Stoll principle is not guaranteed to work when one is interested in expected values instead of densities. Finally, we provide both new applications of the method, and immediate proofs for known results.
