Geodesic
Milne's Correcting Factor and Derived De Rham Cohomology. II
Documenta mathematica, Tome 22 (2017), pp. 1303-1321.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Milne's correcting factor, which appears in the Zeta-value at $s=n$ of a smooth projective variety $X$ over a finite field $\Bbb F_q$, is the Euler characteristic of the derived de Rham cohomology of $X/\Bbb{Z}$ modulo the Hodge filtration $F^n$. In this note, we extend this result to arbitrary separated schemes of finite type over $\Bbb F_q$ 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 $\Bbb Z$ modulo $F^n$.
Classification : 14G10, 14F40, 14G15, 11G25
Keywords: Milne's correcting factor, zeta function, special values, derived de Rham cohomology, cotangent complex, fundamental line, $eh$-topology 
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     author = {Morin, Baptiste},
     title = {Milne's {Correcting} {Factor} and {Derived} {De} {Rham} {Cohomology.} {II}},
     journal = {Documenta mathematica},
     pages = {1303--1321},
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     volume = {22},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a12/}
}
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Morin, Baptiste. Milne's Correcting Factor and Derived De Rham Cohomology. II. Documenta mathematica, Tome 22 (2017), pp. 1303-1321. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a12/