Characteristic Epsilon Cycles of ℓ-adic Sheaves on Varieties

2019/11/06 by Takeuchi, Daichi
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1911.02269

Abstract

Let X be a smooth variety over a finite field \mathbbF_q. Let ℓ be a rational prime number invertible in \mathbbF_q. For an ℓ-adic sheaf F on X, we construct a cycle supported on the singular support of F whose coefficients are ℓ-adic numbers modulo roots of unity. It is a refinement of the characteristic cycle CC(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.

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• Cycle caractéristique sur une puissance symétrique d'une courbe et déterminant de la cohomologie étale