Đề tài " Ramification theory for varieties over a perfect field "

For an -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. Let F be a perfect field and U be a separated and smooth scheme of finite type purely of dimension d over F . In this paper, we study ramification of a finite ´tale scheme V over U along the boundary, by introducing a map ().

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