Hodge and Tate conjectures for hypergeometric sheaves

Details Hodge and Tate conjectures for hypergeometric sheaves Hodge and Tate conjectures for hypergeometric sheaves

1996-08-25

arxiv.org/abs/alg-geom/9705023v3

Mathematics

Algebraic Geometry

42 pages, amstex

Scientific paper

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.

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