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• W3105024405 abstract "A natural question in the theory of Tannakian categories is: What if you don’t remember Forget? Working over an arbitrary commutative ring R, we prove that an answer to this question is given by the functor represented by the étale fundamental groupoid π 1(spec(R)), i.e. the separable absolute Galois group of R when it is a field. This gives a new definition for étale π 1(spec(R)) in terms of the category of R-modules rather than the category of étale covers. More generally, we introduce a new notion of “commutative 2-ring” that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of π 1 for the corresponding “affine 2-schemes.” These results help to simplify and clarify some of the peculiarities of the étale fundamental group. For example, étale fundamental groups are not “true” groups but only profinite groups, and one cannot hope to recover more: the “Tannakian” functor represented by the étale fundamental group of a scheme preserves finite products but not all products." @default.
• W3105024405 created "2020-11-23" @default.
• W3105024405 creator A5074192674 @default.
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• W3105024405 date "2012-01-13" @default.
• W3105024405 modified "2023-09-27" @default.
• W3105024405 title "The Fundamental Pro-groupoid of an Affine 2-scheme" @default.
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• W3105024405 doi "https://doi.org/10.1007/s10485-011-9275-y" @default.
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