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Title:
Hodge Groups of Hodge Structures with Hodge Numbers (n,0,...,0,n)
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Abstract:
We discuss the Hodge groups of simple polarizable Hodge structures with Hodge numbers (n, 0, . . . , 0, n), when n is 1, 4, a prime p, or 2p. The results when n is 1, 4, or p generalize known results about abelian varieties, whereas the results when n is 2p are entirely new. Thus, the results for n = 2p may be applied to simple abelian varieties to yield results about both the Hodge and General Hodge Conjectures for these varieties.
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