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arXiv · 2209.03553

The local motivic monodromy conjecture for simplicial nondegenerate singularities

Matt Larson·Sam Payne·Alan Stapledon
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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 $p$-adic zeta functions for large primes $p$.

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Matt Larson, Sam Payne, Alan Stapledon. 2022-09-08. The local motivic monodromy conjecture for simplicial nondegenerate singularities. https://arxiv.org/abs/2209.03553

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