Abstract
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 objects. In particular, we prove that if G(i) (for i = 1, 2, 3) is an ...
Abstract
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 objects. 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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