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On the relative projective space

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Matias Data and Juliana Osorio

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.

Keywords:
symmetric monoidal category, algebra object, line object, relative scheme

2010 MSC:
14A22, 18F99

*Theory and Applications of Categories,*
Vol. 34, 2019,
No. 3, pp 58-79.

Published 2019-02-22.

http://www.tac.mta.ca/tac/volumes/34/3/34-03.pdf

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