# Lifting Galois sections along torsors

@article{Borne2013LiftingGS, title={Lifting Galois sections along torsors}, author={Niels Borne and M. Emsalem and J. Stix}, journal={Mathematische Nachrichten}, year={2013}, volume={288}, pages={1939-1951} }

The cuspidalization conjecture, which is a consequence of Grothendieck's section conjecture, asserts that for any smooth hyperbolic curve X over a finitely generated field k of characteristic 0 and any non empty Zariski open , every section of lifts to a section of . We consider in this article the problem of lifting Galois sections to the intermediate quotient introduced by Mochizuki [10]. We show that when and is an union of torsion sub-packets every Galois section actually lifts to . One of… Expand

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