Year: 2017
Type: preprint
Abstract: We associate an Albert form to any pair of cyclic algebras of prime degree $p$ over a field $F$ with $\operatorname{char}(F)=p$ which coincides with the classical Albert form when $p=2$. We prove that if every Albert form is isotropic then $H^4(F)=0$. As a result, we obtain that if $F$ is a linked field with $\operatorname{char}(F)=2$ then its $u$-invariant is either $0,2,4$ or $8$.
Source: arXiv (Cornell University)
Authors: Chapman, Adam, Dolphin, Andrew
Institutions: Tel Hai Academic College, Ghent University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Vlaamse regering
OpenAlex ID: W2951549962