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On the Derived Category of 1-motives

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We embed the derived category of Deligne 1-motives over a perfect field into the étale version of Voevodsky's triangulated category of geometric motives, after inverting the exponential characteristic. We then show that this full embedding ``almost'' has a left adjoint LAlb. Applying LAlb to the motive of a variety we get a bounded complex of 1-motives, that we compute fully for smooth varieties and partly for singular varieties. Among applications, we give motivic proofs of Roĭtman type theorems and new cases of Deligne's conjectures on 1-motives.

Author(s): Luca Barbieri-viale, Bruno Kahn
Series: Astérisque 381
Publisher: Société Mathématique de France
Year: 2016

Language: English
Pages: 254
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