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Ramification theory for varieties over a perfect field

Kazuya Kato·Takeshi Saito
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Abstract

For an $\ell$-adic sheaf on a variety of arbitrary dimension over a perfect field, we define the Swan class measuring the wild ramification as a 0-cycle class supported on the ramification locus. We prove a Lefschetz trace formula for open varieties and a generalization of the Grothendieck-Ogg-Shararevich formula using the Swan class.

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Kazuya Kato, Takeshi Saito. 2004-02-02. Ramification theory for varieties over a perfect field. https://arxiv.org/abs/math/0402010

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