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The section conjecture over large algebraic extensions of finitely generated fields

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  • Moshe Jarden
  • Sebastian Petersen

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)$\widetilde{K}({\bf \sigma })$.

Suggested Citation

  • Moshe Jarden & Sebastian Petersen, 2022. "The section conjecture over large algebraic extensions of finitely generated fields," Mathematische Nachrichten, Wiley Blackwell, vol. 295(5), pages 890-911, May.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:5:p:890-911
    DOI: 10.1002/mana.201900538
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