On the "Section Conjecture" in anabelian geometry by Koenigsmann, J

“…The section conjecture in Grothendieck's anabelian geometry says that the sections of the canonical projection from the arithmetic fundamental group of X onto the absolute Galois group of K are (up to conjugation) in one-to-one correspondence with K-rational points of X. …”

Topology of moduli spaces of curves and anabelian geometry in positive characteristic by Zhi Hu, Yu Yang, Runhong Zong

“…It shows that the topology of moduli spaces of curves can be understood from the viewpoint of anabelian geometry. We formulate some new anabelian-geometric conjectures concerning tame fundamental groups of curves over algebraically closed fields of characteristic $p>0$ from the point of view of moduli spaces. …”
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Heights via anabelian geometry and local Bloch-Kato Selmer sets by Betts, L