The monodromy conjecture for remarkable numbers
The monodromy conjecture for remarkable numbers
Let be an -dimensional smooth complex irreducible variety and let be a regular function with non-empty zero locus. Let be a remarkable number of , meaning one of the numbers defined from the combinatorics and vanishing orders associated with a log resolution of . Monodromy conjecture for the remarkable numbers. If is a remarkable number of , then
and is a monodromy eigenvalue on the nearby cycles complex of . This conjecture would produce roots of the -function and monodromy eigenvalues directly from the combinatorial remarkable numbers. The supplied text does not report a resolution.
Sources & referencesView supporting material
Primary source
Nero Budur, Eduardo de Lorenzo Poza, Quan Shi and Huaiqing Zuo, “A remarkable subset of poles of the motivic zeta function”, arXiv:2602.13508 (2026).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.