Biextensions of 1-motives by 1-motives
نویسنده
چکیده
Let S be a scheme. In this paper, we define the notion of biextensions of 1-motives by 1-motives. Moreover, if M(S) denotes the Tannakian category generated by 1-motives over S (in a geometrical sense), we define geometrically the morphisms of M(S) from the tensor product of two 1-motives M1⊗M2 to another 1-motive M3, to be the isomorphism classes of biextensions of (M1, M2) by M3: HomM(S)(M1 ⊗ M2, M3) = Biext (M1, M2;M3) Generalizing this definition we obtain, modulo isogeny, the geometrical notion of morphism of M(S) from a finite tensor product of 1-motives to another 1-motive.
منابع مشابه
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We introduce the notion of biextensions of 1-motives by 1-motives and we define morphisms from the tensor product of two 1-motives to a third 1-motive as isomorphism classes of such biextensions. 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-motiv...
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