Characteristic Epsilon Cycles of $\ell$-adic Sheaves on Varieties

Abstract

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.

arXiv commentThe previous version is divided into 2 parts and this contains the main parts of the previous one. Revised version. arXiv admin note: text overlap with arXiv:1510.03018 by other authors

References in corpus (3)

• Wild ramification determines the characteristic cycle
• Geometric local epsilon factors
• Characteristic class and the epsilon factor of an étale sheaf

Cited by in corpus (1)

• Compatible systems of $\ell$-adic sheaves