Constructs characteristic epsilon cycles for l-adic sheaves on varieties over finite or perfect fields that refine the characteristic cycle CC(F), satisfy Milnor-type formulas for local epsilon factors, and yield a product formula for global epsilon factors modulo roots of unity.
Characteristic class and the epsilon factor of an \'etale sheaf
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abstract
We prove a twist formula for the epsilon factor of a constructible sheaf on a projective smooth variety over a finite field in terms of characteristic class of the sheaf. This formula is a modified version of the formula conjectured by Kato and Saito in [Ann. Math., 168 (2008):33-96, Conjecture 4.3.11]. We give two applications of the twist formula. Firstly, we prove that the characteristic classes of constructible \'etale sheaves on projective smooth varieties over a finite field are compatible with proper push-forward. Secondly, we show that the two Swan classes in the literature are the same on proper smooth surfaces over a finite field.
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2019 1verdicts
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Characteristic Epsilon Cycles of $\ell$-adic Sheaves on Varieties
Constructs characteristic epsilon cycles for l-adic sheaves on varieties over finite or perfect fields that refine the characteristic cycle CC(F), satisfy Milnor-type formulas for local epsilon factors, and yield a product formula for global epsilon factors modulo roots of unity.