  The paper discusses four approaches to the biextension of Chow groups and
their equivalences. These are the following: an explicit construction given by
S.Bloch, a construction in terms of the Poincare biextension of dual
intermediate Jacobians, a construction in terms of K-cohomology, and a
construction in terms of determinant of cohomology of coherent sheaves. A new
approach to J.Franke's Chow categories is given. An explicit formula for the
Weil pairing of algebraic cycles is obtained.
