Extensions and biextensions of locally constant group schemes, tori and abelian schemes

Details Extensions and biextensions of locally constant group schemes, tori and abelian schemes Extensions and biextensions of locally constant group schemes, tori and abelian schemes

2010-07-22

arxiv.org/abs/1007.3875v1

Math. Z. 261 (2009), no. 4, pp. 845--868

Mathematics

Algebraic Geometry

Scientific paper

Let S be a scheme. We compute explicitly the group of homomorphisms, the S-sheaf of homomorphisms, the group of extensions, and the S-sheaf of extensions involving locally constant S-group schemes, abelian S-schemes, and S-tori. Using the obtained results, we study the categories of biextensions involving these geometrical objets. In particular, we prove that if G_i (for i=1,2,3) is an extension of an abelian S-scheme A_i by an S-torus T_i, the category of biextensions of (G_1,G_2) by G_3 is equivalent to the category of biextensions of the underlying abelian S-schemes (A_1,A_2) by the underlying S-torus T_3.

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