# Interesting implications on the theory of motives if the Hodge conjecture holds

For example,

Under the Hodge conjecture the Motivic galois group coincides with Mumford-Tate group.

The Hodge conjecture implies the Lefschetz and Kunneth standard conjectures, as well as conjecture D (for singular cohomology) over fields of characteristic 0.

• Sorry, never mind. I see now that you indeed mean Hodge Conjecture. – M.G. Aug 31 '16 at 6:09