2024/04/04 by Roberto, Kaique Matias de Andrade, Mariano, Hugo Luiz
#Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2404.03785
In this ongoing work, we extend to a class of well-behaved pre-special hyperfields the work of J. Miná\v c and Spira (\citeminac1996witt) that describes a (pro-2)-group of a field extension that encodes the quadratic form theory of a given field F: in \citeadem1999cohomology it is shown that its associated cohomology ring contains a copy of the cohomology ring of the field F. Our construction, a contravariant functor into the category of "pointed" pro-2-groups, is essentially given by generators and relations of profinite-2-groups. We prove that such profinite groups Gal(F) encode the space of orders of the special group canonically associated to the hyperfield F and provide a criterion to detect when F is formally real or not.