Kato–Milne cohomology and polynomial forms

Adam Chapman, Kelly McKinnie

Research output: Contribution to journalArticlepeer-review

Abstract

Given a prime number p, a field F with char(F)=p and a positive integer n, we study the class-preserving modifications of Kato–Milne classes of decomposable differential forms. These modifications demonstrate a natural connection between differential forms and p-regular forms. A p-regular form is defined to be a homogeneous polynomial form of degree p for which there is no nonzero point where all the order p−1 partial derivatives vanish simultaneously. We define a C˜p,m field to be a field over which every p-regular form of dimension greater than pm is isotropic. The main results are that for a C˜p,m field F, the symbol length of Hp 2(F) is bounded from above by pm−1−1 and for any n⩾⌈(m−1)log2⁡(p)⌉+1, Hp n+1(F)=0.

Original languageEnglish
Pages (from-to)3547-3559
Number of pages13
JournalJournal of Pure and Applied Algebra
Volume222
Issue number11
DOIs
StatePublished - Nov 2018

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