Characteristic class and the epsilon factor of an étale sheaf

Umezaki, Naoya; Yang, Enlin; Zhao, Yigeng

doi:10.48550/arxiv.1701.02841

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Cited by 2 publications

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“…A weaker version of Conjecture 2.2.1 is proved in the case k is finite and X and Y are projective in [19] using ε-factors.…”

Section: We Consider the Cartesian Diagrammentioning

confidence: 99%

Characteristic cycles and the conductor of direct image

Saito

2017

Preprint

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We prove the functoriality for proper push-forward of the characteristic cycles of constructible complexes by morphisms of smooth projective schemes over a perfect field, under the assumption that the direct image of the singular support has the dimension at most that of the target of the morphism. The functoriality is deduced from a conductor formula which is a special case for morphisms to curves. The conductor formula in the constant coefficient case gives the geometric case of a formula conjectured by Bloch.

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“…A weaker version of Conjecture 2.2.1 is proved in the case k is finite and X and Y are projective in [19] using ε-factors.…”

Section: We Consider the Cartesian Diagrammentioning

confidence: 99%

Characteristic cycles and the conductor of direct image

Saito

2017

Preprint

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“…In [32], N. Umezaki, E. Yang, and Y. Zhao prove the twist formula of global epsilon factors [32,Theorem 5.23.]. A weaker version modulo roots of unity can be also deduced from the theorem above and Lemma 5.19.1.…”

Section: Introductionmentioning

confidence: 97%

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

Takeuchi¹

2019

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Let X be a smooth variety over a finite field F q . Let ℓ be a rational prime number invertible in F 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.• For the ℓ-adic formalism of a noetherian topos T , we refer to [7], which we review in the appendix. The derived category of constructible complexes of E-sheaves (resp. O E -sheaves) on T is denoted by D b c (T, E) (resp. D b c (T, O E )). We put 0 for objects of D b c (T, O E ) (i.e. F 0 ∈ D b c (T, O E )) and denote F := F 0 ⊗ O E E.

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Characteristic class and the epsilon factor of an étale sheaf

Cited by 2 publications

References 25 publications

Characteristic cycles and the conductor of direct image

Characteristic cycles and the conductor of direct image

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

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