UPDATE (5/3/2014): Now published.
The citation is:
B. Totaro (2014) “Hodge Structures of Type
(n, 0, … , 0, n),” International Mathematics Research Notices, rnu063, 24 pages.
ORIGINAL POST: I’ve posted a new paper on the arXiv:
Hodge structures of type (n,0,…,0,n).
The abstract: This paper determines all the possible endomorphism algebras for polarizable Q-Hodge structures of type (n,0,…,0,n). This generalizes the classification of the possible endomorphism algebras of abelian varieties by Albert and Shimura. As with abelian varieties, the most interesting feature of the classification is that in certain cases, every Hodge structure on which a given algebra acts must have extra endomorphisms.
(“In the crook of his free arm nestled the dignified Hodge.”)