Compatible systems and ramification

2019/10/21 by Qing Lu, Weizhe Zheng · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #advanced mathematical theories

paper · doi:10.1112/s0010437x19007619

Abstract

We show that compatible systems of ℓ -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 ℓ -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.

Citations

• Good Reduction of Abelian Varieties

Cited by

• Slopes and weights of ℓ-adic cohomology of rigid spaces

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