The local motivic monodromy conjecture for simplicial nondegenerate singularities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912910517731328 |
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| author | Larson, Matt Payne, Sam Stapledon, Alan |
| author_facet | Larson, Matt Payne, Sam Stapledon, Alan |
| contents | 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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03553 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The local motivic monodromy conjecture for simplicial nondegenerate singularities Larson, Matt Payne, Sam Stapledon, Alan Algebraic Geometry 14E18, 14G10, 14M25 (Primary) 13F55, 05E45 (Secondary) 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 $p$. |
| title | The local motivic monodromy conjecture for simplicial nondegenerate singularities |
| topic | Algebraic Geometry 14E18, 14G10, 14M25 (Primary) 13F55, 05E45 (Secondary) |
| url | https://arxiv.org/abs/2209.03553 |