Geodesic
Generalized Bockstein maps and Massey products
Forum of Mathematics, Sigma, Tome 11 (2023)

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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 $\mathbb {Q}$ and to give a new proof of the vanishing of Massey triple products in Galois cohomology. 
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     title = {Generalized {Bockstein} maps and {Massey} products},
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Yeuk Hay Joshua Lam; Yuan Liu; Romyar Sharifi; Preston Wake; Jiuya Wang. Generalized Bockstein maps and Massey products. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2022.103

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