  There exists a well-known Lefschetz formula for the number of fixed points in
algebraic topology. In algebraic geometry, there exist cohomologies of coherent
sheaves. It is natural to consider the same alternated sum of traces as in
Lefschetz formula for cohomologies of sheaves. In the present paper, we
consider the case of the action of a one-dimensional torus on a smooth
projectve variety. Using theory of adelic complexes it becomes possible to
rewrite coherent Lefschetz formula in a new compact form and then to prove it.
