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 $\operatorname{DM}_{\rm gm}(k)$.

A note on relative duality for Voevodsky motives / L. Barbieri Viale, B. Kahn. - In: TOHOKU MATHEMATICAL JOURNAL. - ISSN 0040-8735. - 60:3(2008), pp. 349-356.

### A note on relative duality for Voevodsky motives

#### Abstract

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 $\operatorname{DM}_{\rm gm}(k)$.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/53857
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