The notion of biextension of two abelian groups by another abelian group is a classical one coming from [SGA7, VII], later extended by Deligne in [D, 10.2] to the case where K0 and K1 are two complexes of abelian sheaves and H is another abelian sheaf. His result Biext1 (K1 , K2 ; H) ∼ Ext1 (K1 ⊗L K2 , H) suggests that the biextension of two 1-motives is related to their tensor product, which is outside the category of 1-motives for trivial reasons.
Biextensions and 1-motives / C. Bertolin, C. Mazza. - In: OBERWOLFACH REPORTS. - ISSN 1660-8933. - 7:4(2010), pp. 1-1. ((Intervento presentato al convegno Mini-Workshop: 1-Motives tenutosi a Oberfolfach nel 2010 [10.4171/OWR/2010/55].
Biextensions and 1-motives
C. MazzaUltimo
2010
Abstract
The notion of biextension of two abelian groups by another abelian group is a classical one coming from [SGA7, VII], later extended by Deligne in [D, 10.2] to the case where K0 and K1 are two complexes of abelian sheaves and H is another abelian sheaf. His result Biext1 (K1 , K2 ; H) ∼ Ext1 (K1 ⊗L K2 , H) suggests that the biextension of two 1-motives is related to their tensor product, which is outside the category of 1-motives for trivial reasons.
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