The u n -invariant and the symbol length of H n 2 (F)

Adam Chapman, Kelly McKinnie

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Given a field F of char(F) = 2, we define u n (F) to be the maximal dimension of an anisotropic form in Iq n F. For n = 1 it recaptures the definition of u(F). We study the relations between this value and the symbol length of H n 2 (F), denoted by sl n 2 (F). We show for any n ≥ 2 that if 2 n ≤ u n (F) ≤ u 2 (F) < ∞, then (Formula Presented). As a result, if u(F) is finite, then sl n 2 (F) is finite for any n, a fact which was previously proven when char(F) ≠ 2 by Saltman and Krashen. We also show that if sl n 2 (F) = 1, then u n (F) is either 2 n or 2 n+1 .

Original languageEnglish
Pages (from-to)513-521
Number of pages9
JournalProceedings of the American Mathematical Society
Volume147
Issue number2
DOIs
StatePublished - Feb 2019

Keywords

  • Kato-Milne cohomology
  • Quadratic forms
  • Symbol length
  • U-invariant

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