论文标题
从$ p $ - adic代数歧管取样
Sampling from $p$-adic algebraic manifolds
论文作者
论文摘要
我们提出了一种从局部字段定义的代数歧管（仿射或投影）采样点的方法，并具有规定的概率分布。受Breiding和Marigliano在抽样真实代数歧管上的工作的启发，我们的方法利用了将给定品种切成互补维度的随机线性空间。我们还提供了这种采样技术的实现，并证明了其适用于各种环境，包括来自线性$ p $ adic-adic代数群，阿贝尔（Abelian）品种和模块化曲线的采样。
We present a method for sampling points from an algebraic manifold, either affine or projective, defined over a local field, with a prescribed probability distribution. Inspired by the work of Breiding and Marigliano on sampling real algebraic manifolds, our approach leverages slicing the given variety with random linear spaces of complementary dimension. We also provide an implementation of this sampling technique and demonstrate its applicability to various contexts, including sampling from linear $p$-adic algebraic groups, abelian varieties, and modular curves.
