A note on relative duality for Voevodsky motives

Luca Barbieri-Viale (1) , Bruno Kahn (2)

1 Dipartimento di Matematica Pura e Applicata [Padova]
2 IMJ - Institut de Mathématiques de Jussieu

Let X be an n-dimensional smooth proper variety over a field admitting resolution of singularities, and Y,Z two disjoint closed subsets of X. We establish an isomorphism M(X-Z,Y) isomorphic to M(X-Y,Z)^*(n)[2n] in Voevodsky's triangulated category of geometric motives. Here, M(X-Z,Y) is the motive of X -Z relative to its closed subset Y.

Mots clés: motives; duality

Domaines: Géométrie algébrique [math.AG]

Luca Barbieri-Viale, Bruno Kahn. A note on relative duality for Voevodsky motives. Tohoku mathematical journal, 2008, 60 (2), pp.349--356. ⟨hal-00126975⟩