p-Johnson homomorphisms and pro-p groups

2013/11/23 by Masanori Morishita, Morishita, Masanori, Yuji Terashima +1
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1311.5982

Abstract

We propose an approach to study non-Abelian Iwasawa theory, using the idea of Johnson homomorphisms in low dimensional topology. We introduce arithmetic analogues of Johnson homomorphisms/maps, called the p-Johnson homomorphisms/maps, associated to the Zassenhaus filtration of a pro-p Galois group over a Z_p-extension of a number field. We give their cohomological interpretation in terms of Massey products in Galois cohomology.

Related

• Generalized Bockstein maps and Massey products
• Iwasawa λ invariant and Massey product
• Two mod-p Johnson filtrations
• Digraphs, pro-p groups and Massey products in Galois cohomology
• Massey products and the Iwasawa theory of fine Selmer groups