MORIN, Baptiste

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MORIN, Baptiste
Institut de Mathématiques de Bordeaux [IMB]

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Documenta Mathematica. 2016

Universität Bielefeld

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Milne's correcting factor, which appears in the Zeta-value at s = n of a smooth projective variety X over a finite field Fq, is the Euler characteristic of the derived de Rham cohomology of X/Z modulo the Hodge filtration F n. In this note, we extend this result to arbitrary separated schemes of finite type over Fq of dimension at most d, provided resolution of singularities for schemes of dimension at most d holds. More precisely, we show that Geisser's generalization of Milne's factor, whenever it is well defined, is the Euler characteristic of the eh-cohomology with compact support of the derived de Rham complex relative to Z modulo F n .< Leer menos

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MILNE'S CORRECTING FACTOR AND DERIVED DE RHAM COHOMOLOGY II

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