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terminology associated to tori is as follows.

*The integer is called the rank or absolute rank of the torus .
*The torus is said to be split over a field extension if . There is a unique minimal finite extension of over which is split, which is called the splitting field of .
*The -rank of is the maximal rank of a split sub-torus of . A torus is split if and only if its -rank equals its absolute rank.
*A torus is said to be anisotropic if its -rank is zero.

Isogenies

An isogeny

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