Sums of two symbols in K₂(F)/2K₂(F) in characteristic two

2026/04/17 by Demba Barry, Adam Chapman, Ahmed Laghribi · 2 voices
Mathematics · #math.KT #math.NT

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Abstract

In this paper, study sums A=\a,b\₂+\c,d\₂ of two symbols in K₂(F)/2K₂(F) when char(F)=2. We first prove a chain lemma that connects A to B=\α,β\₂+\γ,δ\₂ by a finite sequence of small steps when A ≡ B. We use this lemma to prove that \a,b,c,d\₂ ∈ K₄(F)/2K₄(F) is a well-defined invariant of A, and that this invariant is trivial if and only if A is congruent to a single symbol in K₂(F)/4K₂(F). We also bound the symbol length of C in K₂(F)/2^m K₂(F) from above when C is the sum of up to four symbols in K₂(F)/2^m+1K₂(F).

Citations

• The Cyclicity of Tensor Products of Cyclic p-Algebras
• Symbol Length of Classes in Milnor K-groups
• Motivic cohomology with 𝐙 / 2 -coefficients

Discussions

• Demba Barry, Adam Chapman, Ahmed Laghribi Sums of two symbols in $K_2(F)/2K_2(F)$ in characteristic two https://arxiv.org/abs/2604.15928 [bsky, 0 points, 0 comments]
• Demba Barry, Adam Chapman, Ahmed Laghribi: Sums of two symbols in $K_2(F)/2K_2(F)$ in characteristic two https://arxiv.org/abs/2604.15928 https://arxiv.org/pdf/2604.15928 https://arxiv.org/html/2604.1 [bsky, 0 points, 0 comments]

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