A note on relative duality for Voevodsky motives
Barbieri-Viale, Luca ; Kahn, Bruno
Tohoku Math. J. (2), Tome 60 (2008) no. 1, p. 349-356 / Harvested from Project Euclid
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Let $k$ be a perfect field which admits resolution of singularities in the sense of Friedlander and Voevodsky (for example, $k$ of characteristic $0$). Let $X$ be a smooth proper $k$-variety of pure dimension $n$ and $Y,Z$ two disjoint closed subsets of $X$. We prove an isomorphism \[ M(X-Z,Y)\simeq M(X-Y,Z)^*(n)[2n], \] where $M(X-Z,Y)$ and $M(X-Y,Z)$ are relative Voevodsky motives, defined in his triangulated category $\operatorname{DM}_{\rm gm}(k)$.
Publié le : 2008-05-15
Classification:  Duality,  motives,  14C25 
@article{1223057732,
     author = {Barbieri-Viale, Luca and Kahn, Bruno},
     title = {A note on relative duality for Voevodsky motives},
     journal = {Tohoku Math. J. (2)},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 349-356},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1223057732}
}

Barbieri-Viale, Luca; Kahn, Bruno. A note on relative duality for Voevodsky motives. Tohoku Math. J. (2), Tome 60 (2008) no. 1, pp.  349-356. http://gdmltest.u-ga.fr/item/1223057732/