  A constructible sheaf corresponding to Gel'fand Zelevinski hypergeometric
functions on a torus is called hypergeometric sheaf. We consider Hodge and Tate
conjectrue for hypergeomtric sheaves. Hodge conjecture is formulated in terms
of variation of Hodge strucure and Tate conjecture is done for l-adic sheaves
on an open set of torus. We prove Hodge and Tate conjecture up to Hodge and
Tate cycle of Fermat motifes. We use cohomological Mellin transform to get the
main theorem. This is the final revision for preprint.
