The monodromy conjecture for coherent ideal sheaves
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.
Sources & referencesView supporting material
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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