On the relative projective space

Let $(C,\otimes,1)$ be an abelian symmetric monoidal category satisfying certain exactness conditions. In this paper we define a presheaf $Proj{C}$ on the category of commutative algebras in $C$ and we prove that this functor is a $C$-scheme in the sense of B. Toen and M. Vaquie. We give another def...

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Bibliographic Details
Published in:Theory and applications of categories 2019-01, Vol.34 (3), p.58
Main Authors: Data, Matias, Osorio, Juliana
Format: Article
Language:English
Subjects:
Algebra
Geometry
Symmetry
Online Access:Get full text
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Summary:Let $(C,\otimes,1)$ be an abelian symmetric monoidal category satisfying certain exactness conditions. In this paper we define a presheaf $Proj{C}$ on the category of commutative algebras in $C$ and we prove that this functor is a $C$-scheme in the sense of B. Toen and M. Vaquie. We give another definition and prove that they give isomorphic $C$-schemes. This construction gives us a context of non-associative relative algebraic geometry. The most important example of the construction is the octonionic projective space.
ISSN:1201-561X