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Duality theories for \(p\)-primary étale cohomology. II. (English) Zbl 0651.14011

The author generalizes his duality theorems for smooth varieties in characteristic \(p\) of Part I of this paper [in: Algebraic and topological theories. Papers from the symposium dedicated to the memory of Dr. Takehiko Miyata held in Kinosaki, October 30–November 9, 1984. Tokyo: Kinokuniya Company Ltd. 127–148 (1986; Zbl 0800.14009)] to the case of an arbitrary scheme \(X\) locally of finite type over the base field. These results in turn are a relative version of Milne’s duality theorem [J. S. Milne, Am. J. Math. 108, 297–360 (1986; Zbl 0611.14020)]. The main point is the construction of a “dualizing complex” of \({\mathbb{Z}}/p^ n{\mathbb{Z}}\)-sheaves on the category \(X_{FRP}\) of flat and relatively perfect schemes over X.
Reviewer: F.Herrlich

MSC:

14F30 \(p\)-adic cohomology, crystalline cohomology
14G15 Finite ground fields in algebraic geometry
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References:

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