2018
DOI: 10.1016/j.jpaa.2017.12.022
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Kato–Milne cohomology and polynomial forms

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… Show more

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Cited by 3 publications
(3 citation statements)
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“…As a result, we obtain an upper bound of 2 m · n i=1 ( u(F) 2 −2 i +1) for the symbol length of H n+1 2 m (F). Similarly, over the C p,r -fields F studied in [5], for which the symbol length of H 2 p (F) was bounded from above by p r−1 − 1, the symbol length of H 2 p m (F) is therefore bounded from above by m · (p r−1 − 1).…”
Section: Other Upper Bounds On the Symbol Lengthmentioning
confidence: 96%
“…As a result, we obtain an upper bound of 2 m · n i=1 ( u(F) 2 −2 i +1) for the symbol length of H n+1 2 m (F). Similarly, over the C p,r -fields F studied in [5], for which the symbol length of H 2 p (F) was bounded from above by p r−1 − 1, the symbol length of H 2 p m (F) is therefore bounded from above by m · (p r−1 − 1).…”
Section: Other Upper Bounds On the Symbol Lengthmentioning
confidence: 96%
“…If the solution has w = 0 then, by [2, Lemma 3.5], ϕ 1 , ϕ 2 and ϕ 3 have a common bilinear 1-fold Pfister form as a common factor. By [11,Corollary 6.2], since n 3, the forms ϕ 1 , ϕ 2 and ϕ 3 also have a common right slot, so they have a common right slot regardless of w.…”
Section: Quadratic Pfister Formsmentioning
confidence: 99%
“…(n − 1)-linkage. It is known that inseparable (n − 1)-linkage of quadratic n-fold Pfister forms implies separable (n − 1)-linkage, but the converse is in general not true (see [12], [8], [5], [6], [3] and [1] for references). Question 1.1.…”
Section: Introductionmentioning
confidence: 99%