2022/10/07 by Kaique Matias de Andrade Roberto, Roberto, Kaique Matias de Andrade, Hugo Rafael de Oliveira Ribeiro +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.2210.03784
openalex publication_date 2022/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present we develop a fragment of the theory of superfields, polynomials and Marshall's quotient in order to obtain for general special groups, a proof of the Arason-Pfister Hauptsatz (APH): "if ϕ≠ ∅ is an anisotropic form and ϕ∈ In(F) then dim (ϕ) ≥ 2n". In the process, we also obtain an alternative proof of APH for reduced special groups that avoid the uses of the invariants developed in \citedickmann2000special. The applications of the full Arason-Pfister Hauptsatz leads to interesting properties of graded rings associated to special groups/hyperfields. Keywords: Arason-Pfister Hauptsatz; hyperfields; special groups; Milnor K-theory; graded rings.