Newton 非退化函数的邻近周期公式下降
Descent of nearby cycle formula for Newton non-degenerate functions
AI总结：
本文证明 Newton 非退化函数邻近周期公式及其 motive 版本的下降定理，无需便利条件，并由此推出 Milnor 单值性最大 Jordan 块数公式及单纯形情形下修正的 Steenbrink 猜想。
摘要：
我们证明了原点处 Newton 非退化函数邻近周期公式的下降定理，以及其 motive 版本（不假设便利条件）。该结论在一些论文中被使用却没有任何证明，而由于坐标超平面的存在，其证明相当不平凡；这一点在关于下降定理的文献中被完全忽略。在孤立奇点情形下，利用标准的权重估计，它蕴含了关于 Milnor 单值性具有理论最大尺寸的 Jordan 块数量的某个著名公式。它还证明了 Steenbrink 猜想的一个修正版本，该猜想涉及孤立奇点情形下具有单纯形 Newton 多胞体的非退化函数的谱对（在非单纯形情形下该猜想为假）。
英文摘要：
We prove a descent theorem of nearby cycle formula for Newton non-degenerate functions at the origin as well as its motivic version (without assuming the convenience condition). This is used in some papers without any proof although its proof is quite nontrivial because of the existence of coordinate hyperplanes which is completely neglected in the literature about the descent theorem. In the isolated singularity case, it implies some well-known formula for the number of Jordan blocks of the Milnor monodromy with the theoretically maximal size, using a standard estimate of weights. It also provides a proof of a modified version of the Steenbrink conjecture on spectral pairs for non-degenerate functions with simplicial Newton polytopes in the isolated singularity case (which is false in the non-simplicial case).
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