Local Monodromy of Constructible Sheaves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911355300216832 |
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| author | Nori, Madhav V. Patel, Deepam |
| author_facet | Nori, Madhav V. Patel, Deepam |
| contents | Given a morphism $f: X \rightarrow S$ of complex algebraic varieties and a constructible sheaf $\mathcal{G}$ on $X$, we compute the local monodromy of $Rf_*(\mathcal{G})$ and $Rf_!(\mathcal{G})$ in terms of the local monodromy of $\mathcal{G}$. Our results generalize previous results by Brieskorn, Borel, Clemens, Deligne, Landsman, Griffiths, Grothendieck, and Kashiwara in the setting of quasi-unipotent sheaves. In the following, we consider the general setting of sheaves of $R$-modules for a commutative noetherian ring $R$, and give applications to computing local monodromy of abelian covers in a uniform manner. We also obtain applications in the context of `generalized Alexander modules' and intersection cohomology with torsion coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02178 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local Monodromy of Constructible Sheaves Nori, Madhav V. Patel, Deepam Algebraic Geometry Given a morphism $f: X \rightarrow S$ of complex algebraic varieties and a constructible sheaf $\mathcal{G}$ on $X$, we compute the local monodromy of $Rf_*(\mathcal{G})$ and $Rf_!(\mathcal{G})$ in terms of the local monodromy of $\mathcal{G}$. Our results generalize previous results by Brieskorn, Borel, Clemens, Deligne, Landsman, Griffiths, Grothendieck, and Kashiwara in the setting of quasi-unipotent sheaves. In the following, we consider the general setting of sheaves of $R$-modules for a commutative noetherian ring $R$, and give applications to computing local monodromy of abelian covers in a uniform manner. We also obtain applications in the context of `generalized Alexander modules' and intersection cohomology with torsion coefficients. |
| title | Local Monodromy of Constructible Sheaves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.02178 |