We consider the category of Deligne 1-motives over
a perfect field k of exponential characteristic p and its derived
category for a suitable exact structure after inverting p. As a
first result, we provide a fully faithful embedding into an ´etale
version of Voevodsky’s triangulated category of geometric motives.
Our second main result is that this full embedding “almost” has
a left adjoint. Applying it 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 Roˇıtman type theorems and new cases of
Deligne’s conjectures on 1-motives.
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原文发布时间:2010/9/1
引用本文:
Luca Barbieri-Viale;Bruno Kahn .On the derived category of 1-motives.http://hftc.firstlight.cn/View.aspx?infoid=994816&cb=wxm2010.
发布时间:2010/9/1.检索时间:2024/12/14