The local motivic monodromy conjecture for simplicial nondegenerate singularities
Algebraic Geometry
2026-02-19 v3
Abstract
We prove the local motivic monodromy conjecture for singularities that are nondegenerate with respect to a simplicial Newton polyhedron. It follows that all poles of the local topological zeta functions of such singularities correspond to eigenvalues of monodromy acting on the cohomology of the Milnor fiber of some nearby point, as do the poles of Igusa's local -adic zeta functions for large primes .
Keywords
Cite
@article{arxiv.2209.03553,
title = {The local motivic monodromy conjecture for simplicial nondegenerate singularities},
author = {Matt Larson and Sam Payne and Alan Stapledon},
journal= {arXiv preprint arXiv:2209.03553},
year = {2026}
}
Comments
v3: Expanded introduction, added examples, and simplified section 4. Final version to appear in Comm. Amer. Math. Soc