MILNE'S CORRECTING FACTOR AND DERIVED DE RHAM COHOMOLOGY II
Language
en
Article de revue
This item was published in
Documenta Mathematica. 2016
Universität Bielefeld
English Abstract
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 ...Read more >
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 .Read less <
Origin
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