Generalized Bockstein maps and Massey products

Yeuk Hay Joshua Lam, Yuan Liu, Romyar Sharifi, Preston Wake, Jiuya Wang

Research output: Contribution to journalArticlepeer-review


Given a profinite group G of finite p-cohomological dimension and a pro-p quotient H of G by a closed normal subgroup N, we study the filtration on the Iwasawa cohomology of N by powers of the augmentation ideal in the group algebra of H. We show that the graded pieces are related to the cohomology of G via analogues of Bockstein maps for the powers of the augmentation ideal. For certain groups H, we relate the values of these generalized Bockstein maps to Massey products relative to a restricted class of defining systems depending on H. We apply our study to prove lower bounds on the p-ranks of class groups of certain nonabelian extensions of and to give a new proof of the vanishing of Massey triple products in Galois cohomology.

Original languageEnglish (US)
Article numberA1
JournalForum of Mathematics, Sigma
StatePublished - Jan 23 2023


  • 20J05 20J06 12G05 11R23 11R34

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


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