On the relative projective space

OSORIO MORALES, JULIANA; DATA, MATIAS

THEORY AND APPLICATIONS OF CATEGORIES

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Año: 2019 vol. 34 p. 58 - 79

1201-561X

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.