A curve satisfies the locally geometric Section Conjecture if it satisfies Kim's conjecture for almost all p, with generalization to S-integral points and verification for the thrice-punctured line over Z[1/2].
The polylog quotient a nd the Gon- charov quotient in computational Chabauty–Kim Theory I
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Chabauty--Kim, finite descent, and the Section Conjecture for locally geometric sections
A curve satisfies the locally geometric Section Conjecture if it satisfies Kim's conjecture for almost all p, with generalization to S-integral points and verification for the thrice-punctured line over Z[1/2].