Serie : Astérisque. Vol 381
Paru le 05/09/2016 | Broché 254 pages
Professionnels
We embed the derived category of Deligne 1-motives over a perfect field into the étale version of Voevodsky's trian- gulated category of géométrie motives, after inverting the exponential characteristic. We then show that this full em- bedding « 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 Roïtman type theorems and new cases of Deligne's conjectures on 1-motives.
