Milne's Correcting Factor and Derived De Rham Cohomology. II
Milne's correcting factor, which appears in the Zeta-value at of a smooth projective variety over a finite field , is the Euler characteristic of the derived de Rham cohomology of modulo the Hodge filtration . In this note, we extend this result to arbitrary separated schemes of finite type over of dimension at most , provided resolution of singularities for schemes of dimension at most holds. More precisely, we show that Geisser's generalization of Milne's factor, whenever it is well defined, is the Euler characteristic of the -cohomology with compact support of the derived de Rham complex relative to modulo .
Cite this article
Baptiste Morin, Milne's Correcting Factor and Derived De Rham Cohomology. II. Doc. Math. 22 (2017), pp. 1303–1321DOI 10.4171/DM/597