| 31. | Any abelian variety is isogenous to a product of simple abelian varieties.
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| 32. | Free abelian groups have properties which make them similar to vector spaces.
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| 33. | More generally, every finitely-generated free abelian group.
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| 34. | On the other hand, an abelian scheme may not be projective.
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| 35. | The locally compact abelian case is part of the Pontryagin duality theory.
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| 36. | This work on the equations defining abelian varieties appeared in 1966 7.
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| 37. | So " C " naturally sits inside an abelian category.
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| 38. | From the category of topological spaces to the category of abelian groups.
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| 39. | The number of independent generators is the rank of an abelian group.
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| 40. | All Abelian groups have only one-dimensional irreducible representations.
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