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arxiv: math/0702661 · v5 · submitted 2007-02-22 · 🧮 math.NT · math.AG

Multilinear morphisms between 1-motives

classification 🧮 math.NT math.AG
keywords motivesmorphismsproducttensorbiextensionsdefinegeometricalmotive
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Let S be an arbitrary scheme. We define biextensions of 1-motives by 1-motives which we see as the geometrical origin of morphisms from the tensor product of two 1-motives to a third one. If S is the spectrum of a field of characteristic 0, we check that these biextensions define morphisms from the tensor product of the realizations of two 1-motives to the realization of a third 1-motive. Generalizing we obtain the geometrical notion of morphisms from a finite tensor product of 1-motives to another 1-motive.

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