The quasi-finite fundamental group scheme conjecture for affine space
The quasi-finite fundamental group scheme conjecture for affine space
Let be the base ring, let be its fraction field, and let be -dimensional affine space with origin . Write for the quasi-finite fundamental group scheme of at the origin, and let denote the fundamental group scheme of the generic fibre at the origin. Quasi-finite fundamental group scheme conjecture. The faithfully flat morphism
is an isomorphism. The conjecture proposes that the quasi-finite fundamental group scheme over the affine space extends without acquiring additional structure after passage to the generic fibre; the source states that it is not proved, while noting that in characteristic the statement is empty.
Sources & referencesView supporting material
Primary source
Marco Antei and Jorge A. Esquivel A, “Models of torsors over affine spaces”, arXiv:1809.06236 (2018).
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