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.
References
Primary source
Marco Antei and Jorge A. Esquivel A, “Models of torsors over affine spaces”, arXiv:1809.06236 (2018).
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