The geometrically m-step solvable Grothendieck conjecture for genus 0 curves over finitely generated fields
Naganori Yamaguchi
TL;DR
This paper proves the geometrically 3-step solvable Grothendieck conjecture for genus 0 curves over finitely generated fields, advancing understanding in anabelian geometry.
Contribution
It establishes the conjecture for genus 0 curves over finitely generated fields in arbitrary characteristic, providing new partial results in anabelian geometry.
Findings
Proves the 3-step solvable Grothendieck conjecture for genus 0 curves
Extends results to fields finitely generated over prime fields
Works in arbitrary characteristic
Abstract
In this paper, we present some partial results for the geometrically m-step solvable Grothendieck conjecture in anabelian geometry. Among other things, we prove the geometrically 3-step solvable Grothendieck conjecture for genus 0 curves over fields finitely generated over the prime field of arbitrary characteristic.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Geometric and Algebraic Topology