The Galois group of a Special Group
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911828439728128 |
|---|---|
| author | Roberto, Kaique Matias de Andrade Mariano, Hugo Luiz |
| author_facet | Roberto, Kaique Matias de Andrade Mariano, Hugo Luiz |
| contents | In this ongoing work, we extend to a class of well-behaved pre-special hyperfields the work of J. Miná\v c and Spira (\cite{minac1996witt}) that describes a (pro-2)-group of a field extension that encodes the quadratic form theory of a given field $F$: in \cite{adem1999cohomology} 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 $\mbox{Gal}(F)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Galois group of a Special Group Roberto, Kaique Matias de Andrade Mariano, Hugo Luiz Commutative Algebra K-Theory and Homology Rings and Algebras In this ongoing work, we extend to a class of well-behaved pre-special hyperfields the work of J. Miná\v c and Spira (\cite{minac1996witt}) that describes a (pro-2)-group of a field extension that encodes the quadratic form theory of a given field $F$: in \cite{adem1999cohomology} 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 $\mbox{Gal}(F)$ 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. |
| title | The Galois group of a Special Group |
| topic | Commutative Algebra K-Theory and Homology Rings and Algebras |
| url | https://arxiv.org/abs/2404.03785 |