Arithmetic cohomology over finite fields and special values of $\zeta$ -functions
Geisser, Thomas
Duke Math. J., Tome 131 (2006) no. 1, p. 27-57 / Harvested from Project Euclid
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We construct cohomology groups with compact support $H^i_c(X_{\rm ar},{\mathbb Z}(n))$ for separated schemes of finite type over a finite field which generalize Lichtenbaum's Weil-étale cohomology groups for smooth and projective schemes (see [22]). In particular, if Tate's conjecture holds, and rational and numerical equivalence agree up to torsion, then the groups $H^i_c(X_{\rm ar},{\mathbb Z}(n))$ are finitely generated, form an integral model of $l$ -adic cohomology with compact support, and admit a formula for the special values of the $\zeta$ -function of $X$
Publié le : 2006-05-15
Classification:  14F20,  14F42,  11G25 
@article{1145452055,
     author = {Geisser, Thomas},
     title = {Arithmetic cohomology over finite fields and special values of $\zeta$ -functions},
     journal = {Duke Math. J.},
     volume = {131},
     number = {1},
     year = {2006},
     pages = { 27-57},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1145452055}
}

Geisser, Thomas. Arithmetic cohomology over finite fields and special values of $\zeta$ -functions. Duke Math. J., Tome 131 (2006) no. 1, pp.  27-57. http://gdmltest.u-ga.fr/item/1145452055/