The Galois action on geometric lattices and the mod-$\ell$ I/OM

Abstract

This paper studies the Galois action on a special lattice of geometric origin, which is related to mod-$\ell$ abelian-by-central quotients of geometric fundamental groups of varieties. As a consequence, we formulate and prove the mod-$\ell$ abelian-by-central variant/strengthening of a conjecture due to Ihara/Oda-Matsumoto.

arXiv commentFinal version. Minor changes/corrections, introduction expanded. Will appear in Inventiones

References in corpus (1)

• Commuting-Liftable Subgroups of Galois Groups II