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We use constructions of versal cohomology classes based on a new notion of ‘presentable functors’, to describe a relationship between the problems of bounding symbol length in cohomology and of finding the minimal degree of a splitting field. The constructions involved are then also used to describe generic splitting varieties for degree 2 cohomology with coefficients in a commutative algebraic group of multiplicative type.

Period and index, symbol lengths, and generic splittings in Galois cohomology