Geodesic
On the relative projective space
Theory and applications of categories, Tome 34 (2019), pp. 58-79

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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.

Publié le :
Classification : 14A22, 18F99
Keywords: symmetric monoidal category, algebra object, line object, relative scheme 
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     author = {Matias Data and Juliana Osorio},
     title = {On the relative projective space},
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     volume = {34},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a2/}
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Matias Data; Juliana Osorio. On the relative projective space. Theory and applications of categories, Tome 34 (2019), pp. 58-79. http://geodesic.mathdoc.fr/item/TAC_2019_34_a2/