  We introduce the "sharp" (universal) extension of a 1-motive (with additive
factors and torsion) over a field of characteristic zero. We define the "sharp
de Rham realization" by passing to the Lie-algebra. Over the complex numbers we
then show a (sharp de Rham) comparison theorem in the category of formal Hodge
structures. For a free 1-motive along with its Cartier dual we get a canonical
connection on their sharp extensions yielding a perfect pairing on sharp
realizations. We thus provide "one-dimensional sharp de Rham cohomology" of
algebraic varieties.
