@inproceedings{7797108a7152457484529008eb1fc69b,

title = "On the symbol length of symbols",

abstract = "Fix a prime p and let F be a field with characteristic not p. Let GF be the absolute Galois group of F, and let μps be the GF -module of roots of unity of order dividing ps in a fixed algebraic closure of F. Let α ∈ Hn(F, μ⊗nps) be a symbol (i.e., α=a1 ∪··· ∪ an where ai ∈ H1(F, μps)) with effective exponent dividing ps−1 (that is ps−1α=0 ∈ Hn(GF, μ⊗np). In this work, we show how to write α as a sum of symbols coming from Hn(F, μ⊗n ps−1), that is, symbols of the form pγ for γ ∈Hn(F, μ⊗nps). If n>3 and p=2, we assume F is prime to p closed and of characteristic zero. In the case p=2, we also bound the symbol length of a sum of two symbols with effective exponent dividing ps−1.",

keywords = "Galois cohomology, Milnor K-theory, higher symbols, quadratic forms",

author = "Eliyahu Matzri",

note = "Publisher Copyright: {\textcopyright} 2024 Eliyahu Matzri.; Amitsur Centennial Symposium, 2021 ; Conference date: 01-11-2021 Through 04-11-2021",

year = "2024",

language = "الإنجليزيّة",

isbn = "9781470475550",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "219--231",

editor = "Avinoam Mann and Rowen, {Louis H.} and Saltman, {David J.} and Aner Shalev and Small, {Lance W.} and Uzi Vishne",

booktitle = "Amitsur Centennial Symposium, 2021",

address = "الولايات المتّحدة",

}