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Pré-Publication, Document De Travail Année : 2005

The boundary motive: definition and basic properties

Résumé

We introduce the notion of the boundary motive of a scheme X over a perfect field. By definition, it measures the difference between the motive X and the motive with compact support of X. We develop three tools to compute the boundary motive in terms of the geometry of a compactification of X: co-localization, invariance under abstract blow-up, and analytical invariance. We then prove auto-duality of the boundary motive of a smooth scheme X. As a formal consequence of this, and of co-localization, we obtain a fourth computational tool, namely localization for the boundary motive.

Dates et versions

hal-00012925 , version 1 (29-10-2005)

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Jörg Wildeshaus. The boundary motive: definition and basic properties. 2005. ⟨hal-00012925⟩
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