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On the derived category of 1-motives

http://www.firstlight.cn2010/12/3

[作者] Luca Barbieri-Viale Bruno Kahn

[摘要] 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.

[关键词] derived category of 1-motives

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-motiveshttp://hftc.firstlight.cn/View.aspx?infoid=994816&cb=wxm2010
发布时间:2010/9/1.检索时间:2024/12/14

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