On the Derived Category of 1-motives

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On the Derived Category of 1-motives (Asterisque) by Luca Barbieri-viale and Bruno Kahn
English | 2016 | ISBN: 2856298370 | 254 pages | PDF | 2 MB

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 Ro?tman type theorems and new cases of Deligne's conjectures on 1-motives.

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