I can't tell from a superficial inspection whether this is correct (such spectacular claims require a great deal of prudence, although superficially it seems to make sense, and the authors obviously aren't crackpots); but if it is, (a) its authors might be eligible for a $1000000 prize and (b) a number of people I know will be quite disappointed.
Update: The authors just posted a revised version
of the article, with the following comment: We no longer claim to
have disproved the Hodge conjecture. Section 5 is deleted except for
5.3, and Theorems 6.2,6.3 are deleted.