论文标题
对不完整品种的阿尔巴尼斯基本变更的完整答案
A complete answer to Albanese base change for incomplete varieties
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Albanese varieties provide a standard tool in algebraic geometry for converting questions about varieties in general, to questions about Abelian varieties. A result of Serre provides the existence of an Albanese variety for any geometrically connected and geometrically reduced scheme of finite type over a field, and a result of Grothendieck--Conrad establishes that Albanese varieties are stable under base change of field provided the scheme is, in addition, proper. A result of Raynaud shows that base change can fail for Albanese varieties without this properness hypothesis. In this paper we show that Albanese varieties of geometrically connected and geometrically reduced schemes of finite type over a field are stable under separable field extensions. We also show that the failure of base change in general is explained by the L/K-image for purely inseparable extensions L/K.
