Let X be a curve over a field k finitely generated over ℚ and t an indeterminate. We prove that, if s is a section of π1(X) → Gal (k) such that the base change sk(t) is birationally liftable, then s comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.
On the birational section conjecture with strong birationality assumptions
BRESCIANI, GIULIO
2024
Abstract
Let X be a curve over a field k finitely generated over ℚ and t an indeterminate. We prove that, if s is a section of π1(X) → Gal (k) such that the base change sk(t) is birationally liftable, then s comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.File in questo prodotto:
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Bresciani - On the birational section conjecture with strong birationality assumptions.pdf
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