Characteristic Epsilon Cycles of $\ell$-adic Sheaves on Varieties
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866910098242142208 |
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| author | Takeuchi, Daichi |
| author_facet | Takeuchi, Daichi |
| contents | Let $X$ be a smooth variety over a finite field $\mathbb{F}_q$. Let $\ell$ be a rational prime number invertible in $\mathbb{F}_q$. For an $\ell$-adic sheaf $\mathcal{F}$ on $X$, we construct a cycle supported on the singular support of $\mathcal{F}$ whose coefficients are $\ell$-adic numbers modulo roots of unity. It is a refinement of the characteristic cycle $CC(\mathcal{F})$, in the sense that it satisfies a Milnor-type formula for local epsilon factors. After establishing fundamental results on the cycles, we prove a product formula of global epsilon factors modulo roots of unity. We also give a generalization of the results to varieties over general perfect fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_02269 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Characteristic Epsilon Cycles of $\ell$-adic Sheaves on Varieties Takeuchi, Daichi Algebraic Geometry Number Theory Let $X$ be a smooth variety over a finite field $\mathbb{F}_q$. Let $\ell$ be a rational prime number invertible in $\mathbb{F}_q$. For an $\ell$-adic sheaf $\mathcal{F}$ on $X$, we construct a cycle supported on the singular support of $\mathcal{F}$ whose coefficients are $\ell$-adic numbers modulo roots of unity. It is a refinement of the characteristic cycle $CC(\mathcal{F})$, in the sense that it satisfies a Milnor-type formula for local epsilon factors. After establishing fundamental results on the cycles, we prove a product formula of global epsilon factors modulo roots of unity. We also give a generalization of the results to varieties over general perfect fields. |
| title | Characteristic Epsilon Cycles of $\ell$-adic Sheaves on Varieties |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/1911.02269 |