## The Hodge Conjecture for Abelian

- 1. ABELIAN
- 1997

We show that if A is an abelian variety over a subfield F of C, and A has purely multiplicative reduction at a discrete valuation of F , then the Hodge group of A is semisimple (Theorem 4.1). Since the non-semisimplicity of the Hodge group of an abelian variety can be translated into a condition on the endomorphism algebra and its action on the tangent… (More)

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