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- W2999414144 abstract "Consider the abelian category π of commutative group schemes of finite type over a field k, its full subcategory β± of finite group schemes, and the associated pro-category Pro(π) (resp. Pro(β±)) of pro-algebraic (resp. profinite) group schemes. When k is perfect, we show that the profinite fundamental group Ο 1 :Pro(π)βPro(β±) is left exact and commutes with base change under algebraic field extensions; as a consequence, the higher profinite homotopy functors Ο i vanish for iβ₯2. Along the way, we describe the indecomposable projective objects of Pro(π) over an arbitrary field k." @default.
- W2999414144 created "2020-01-23" @default.
- W2999414144 creator A5037254348 @default.
- W2999414144 date "2020-01-16" @default.
- W2999414144 modified "2023-10-02" @default.
- W2999414144 title "On the fundamental groups of commutative algebraic groups" @default.
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- W2999414144 doi "https://doi.org/10.5802/ahl.25" @default.
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