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arXiv · 1911.04737

Wild ramification, the nearby cycle complexes, and the characteristic cycles of $\ell$-adic sheaves

Hiroki Kato
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Abstract

We prove a purely local form of a result of Saito and Yatagawa. They proved that the characteristic cycle of a constructible étale sheaf is determined by wild ramification of the sheaf along the boundary of a compactification. But they had to consider ramification at all the points of the compactification. We give a pointwise result, that is, we prove that the characteristic cycle of a constructible étale sheaf around a point is determined by wild ramification at the point. The key ingredient is to prove that wild ramification of the stalk of the nearby cycle complex of a constructible étale sheaf at a point is determined by wild ramification at the point.

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Hiroki Kato. 2019-11-12. Wild ramification, the nearby cycle complexes, and the characteristic cycles of $\ell$-adic sheaves. https://doi.org/10.2140/ant.2021.15.1523

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