Tohoku Mathematical Journal

A note on relative duality for Voevodsky motives

Luca Barbieri-Viale and Bruno Kahn

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

Article information

Source
Tohoku Math. J. (2), Volume 60, Number 3 (2008), 349-356.

Dates
First available in Project Euclid: 3 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1223057732

Digital Object Identifier
doi:10.2748/tmj/1223057732

Mathematical Reviews number (MathSciNet)
MR2453727

Zentralblatt MATH identifier
1152.14007

Subjects
Primary: 14C25: Algebraic cycles

Keywords
Duality motives

Citation

Barbieri-Viale, Luca; Kahn, Bruno. A note on relative duality for Voevodsky motives. Tohoku Math. J. (2) 60 (2008), no. 3, 349--356. doi:10.2748/tmj/1223057732. https://projecteuclid.org/euclid.tmj/1223057732


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References

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