The cuspidalisation of sections of arithmetic fundamental groups II

Abstract

In this paper we investigate the theory of cuspidalisation of sections of arithmetic fundamental groups of hyperbolic curves to cuspidally i-th and 2/p-th step prosolvable arithmetic fundamental groups. As a consequence we exhibit two, necessary and sufficient, conditions for sections of arithmetic fundamental groups of hyperbolic curves over p-adic local fields to arise from rational points. We also exhibit a class of sections of arithmetic fundamental groups of p-adic curves which are orthogonal to Pic, and which satisfy (unconditionally) one of the above conditions.

References in corpus (1)

• Galois sections for abelianized fundamental groups

Cited by in corpus (1)

• On the birational section conjecture over finitely generated fields