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arXiv · 1801.03221

Compatible systems and ramification

Qing Lu·Weizhe Zheng
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Abstract

We show that compatible systems of $\ell$-adic sheaves on a scheme of finite type over the ring of integers of a local field are compatible along the boundary up to stratification. This extends a theorem of Deligne on curves over a finite field. As an application, we deduce the equicharacteristic case of classical conjectures on $\ell$-independence for proper smooth varieties over complete discrete valuation fields. Moreover, we show that compatible systems have compatible ramification. We also prove an analogue for integrality along the boundary.

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Qing Lu, Weizhe Zheng. 2018-01-10. Compatible systems and ramification. https://doi.org/10.1112/s0010437x19007619

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