The monodromy conjecture for coherent ideal sheaves
Let be a smooth irreducible complex variety and let be a coherent ideal sheaf of with a non-empty zero locus. Let be its motivic zeta function, and let denote the set of Verdier monodromy eigenvalues of . Monodromy conjecture. If is a pole of , then
This conjecture relates poles of motivic zeta functions to Verdier monodromy. The source presents it as an established conjecture; its resolution status is not specified in the supplied text.
References
Primary source
Yifan Chen, Quan Shi, Yongxin Xu and Huaiqing Zuo, “On the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals”, arXiv:2511.01262 (2025).
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