Abstract
Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group G F , and let H n denote its mod p cohomology group H n (G F ,Z/pZ). The triple Massey product of weight (n,k,m)∈N 3 is a partially defined, multi-valued function 〈⋅,⋅,⋅〉:H n ×H k ×H m →H n+k+m−1 . In this work we prove that for an arbitrary prime p, any defined 3MP of weight (n,1,m), where the first and third entries are symbols, contains zero; and that any defined 3MP of weight (1,k,1), where the middle entry is a symbol, contains zero.
| Original language | English |
|---|---|
| Pages (from-to) | 136-146 |
| Number of pages | 11 |
| Journal | Journal of Algebra |
| Volume | 527 |
| DOIs | |
| State | Published - 1 Jun 2019 |
Bibliographical note
Publisher Copyright:© 2019 Elsevier Inc.
Funding
The author would like to thank I. Efrat for many interesting discussions and helpful suggestions and to S. Gille for helpful conversations at the conference “Nilpotent Fundamental Groups” held at BIRS. The author also thanks the anonymous referee for helpful remarks and suggestions in particular for his remarks on the proof of the characteristic 2 case of Lemma 4.1. This research was supported by the Israel Science Foundation(grant No. 630/17).
| Funders | Funder number |
|---|---|
| Israel Science Foundation | 630/17 |
Keywords
- External cohomological operations
- Galois cohomology
- Massey products
- Symbols