Essential dimension of algebraic groups

The essential dimension of an algebraic object is roughly speaking, the number of algebraically independent parameters needed to ”describe” that object. It was first introduced by Buhler and Reichstein in 1997 for Galois field extensions, but since has been studied for algebraic groups. Using data given by integral representations and lattices, one can attain bounds on the essential dimension of a particular type of algebraic group, namely extensions of finite groups by algebraic tori.

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