Homological interpretation of extensions and biextensions of complexes

Details Homological interpretation of extensions and biextensions of complexes Homological interpretation of extensions and biextensions of complexes

2008-08-24

arxiv.org/abs/0808.3267v3

Mathematics

Algebraic Geometry

29 pages

Scientific paper

Let T be a topos. Let K_i=[A_i \to B_i] (for $i=1,2,3$) be a complex of commutative groups of T with A_i in degree 1 and B_i in degree 0. We define the geometrical notions of extension of K_1 by K_3 and of biextension of (K_1,K_2) by K_3. These two notions generalize to complexes of the kind K_i the classical notions of extensions and biextensions of commutative groups of T. We then apply the geometrical-homological principle of Grothendieck in order to compute the homological interpretation of extensions and biextensions of complexes.

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