We explain how the Riemann-Roch theorem for divisors on an abelian variety $A$ is related to the reduced norms of the Wedderburn components of $\End^0(A)$ the $\QQ$-endomorphism algebra of $A$. We then describe some consequences and examples.
Rational curves on quotients of abelian varieties by finite groups
Polarizations on abelian varieties
Some elementary theorems about divisibility of 0-cycles on abelian varieties defined over finite fields
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