Metadata
Abstract
Consider the abelian category of commutative group schemes of finite type over a field , its full subcategory of finite group schemes, and the associated pro-category (resp. ) of pro-algebraic (resp. profinite) group schemes. When is perfect, we show that the profinite fundamental group is left exact and commutes with base change under algebraic field extensions; as a consequence, the higher profinite homotopy functors vanish for . Along the way, we describe the indecomposable projective objects of over an arbitrary field .
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