Motivic nearby cycles and their monodromy at a singular point
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908643601940480 |
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| author | Azouri, Ran |
| author_facet | Azouri, Ran |
| contents | In this survey, we explain how to compute both the quadratic Euler characteristic of nearby cycles, and the motivic monodromy, at a quasi-homogeneous singularity. This gives, for such singularity, a quadratic refinement to the Deligne--Milnor formula in characteristic zero, and an enhancement of the Picard--Lefschetz formula to Voevodsky motives with rational coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Motivic nearby cycles and their monodromy at a singular point Azouri, Ran Algebraic Geometry Algebraic Topology K-Theory and Homology 14B05, 14F42 (Primary) 19E15, 19G12, 32S55 (Secondary) In this survey, we explain how to compute both the quadratic Euler characteristic of nearby cycles, and the motivic monodromy, at a quasi-homogeneous singularity. This gives, for such singularity, a quadratic refinement to the Deligne--Milnor formula in characteristic zero, and an enhancement of the Picard--Lefschetz formula to Voevodsky motives with rational coefficients. |
| title | Motivic nearby cycles and their monodromy at a singular point |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology 14B05, 14F42 (Primary) 19E15, 19G12, 32S55 (Secondary) |
| url | https://arxiv.org/abs/2511.07668 |