TY - JOUR

T1 - Kato–Milne cohomology and polynomial forms

AU - Chapman, Adam

AU - McKinnie, Kelly

N1 - Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2018/11

Y1 - 2018/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85039792380&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2017.12.022

DO - 10.1016/j.jpaa.2017.12.022

M3 - Article

AN - SCOPUS:85039792380

SN - 0022-4049

VL - 222

SP - 3547

EP - 3559

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 11

ER -