Geodesic
Milne's Correcting Factor and Derived De Rham Cohomology. II
Documenta mathematica, Tome 22 (2017), pp. 1303-1321
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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 Fn. 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 Fn.
DOI : 10.4171/dm/597
Classification : 11G25, 14F40, 14G10, 14G15
Mots-clés : zeta function, special values, derived de Rham cohomology, Milne's correcting factor, cotangent complex, fundamental line, eh-topology 
@article{10_4171_dm_597,
     author = {Baptiste Morin},
     title = {Milne's {Correcting} {Factor} and {Derived} {De} {Rham} {Cohomology.} {II}},
     journal = {Documenta mathematica},
     pages = {1303--1321},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/597},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/597/}
}
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Baptiste Morin. Milne's Correcting Factor and Derived De Rham Cohomology. II. Documenta mathematica, Tome 22 (2017), pp. 1303-1321. doi: 10.4171/dm/597

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