发表机构
KU Leuven; Institute of Mathematics, Vietnam Academy of Science and Technology; Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo; Department of Mathematics, Graduate School of Science, the University of Osaka（荷语鲁汶大学; 越南科学技术院数学研究所; 东京大学宇宙物理数学研究所（Kavli）; 大阪大学理学研究科数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推广p进McKay对应，将Denef的Igusa局部zeta函数公式拓展至Q-嵌入奇点消解情形，证明了相关强单值群猜想与指数和猜想对特定加权齐次多项式成立。
AI 中文摘要
1991年，Denef针对具有好约化的p进域上的奇点嵌入消解，给出了Igusa局部zeta函数的显式公式。本文通过略微推广第二作者在2017年提出的p进McKay对应，将Denef的结果推广到Q-嵌入奇点消解的情形。因此，关于Igusa局部zeta函数的强单值群猜想，对具有孤立奇点的加权齐次多项式成立。此外，我们利用所得公式，证明了非退化且具有孤立奇点的加权齐次多项式情形下的Igusa指数和猜想。
英文摘要
In 1991, Denef introduced an explicit formula for Igusa's local zeta functions in terms of embedded resolutions of singularities over $p$-adic fields with good reduction. In this paper, by slightly generalizing the $p$-adic McKay correspondence given by the second author in 2017, we extend Denef's result to the setting of $\mathbb{Q}$-embedded resolutions of singularities. Consequently, the strong monodromy conjecture with respect to Igusa's local zeta functions holds for weighted homogeneous polynomials with isolated singularities. Moreover, we use our formula to prove Igusa's conjecture for exponential sums in the case of non-degenerate weighted homogeneous polynomials with isolated singularities.
Comments48 pages. Comments are welcome
