The section conjecture over large algebraic extensions of finitely generated fields

Moshe Jarden and Sebastian Petersen

Mathematische Nachrichten, 2022, vol. 295, issue 5, 890-911

Abstract: Let K be a finitely generated extension of its prime field and let e≥2$e\ge 2$ be an integer. We prove the injectivity part of the section conjecture of Grothendieck for almost all σ:=(σ1,…,σe)∈Gal(K)e${\bf \sigma }:=\big (\sigma _1,\ldots ,\sigma _e\big )\in {\rm Gal}(K)^e$ and for all smooth geometrically integral projective curves of genus ≥1 over the field K∼(σ)$\widetilde{K}({\bf \sigma })$.

Date: 2022
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https://doi.org/10.1002/mana.201900538

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