Reconstruction theorem for monoid schemes

2020/02/11 by Ilia Pirashvili, Pirashvili, Ilia
Mathematics · #18B25 #20M14 #20M30 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #math.AG #math.CT #msc:18B25 #msc:20M14 #msc:20M30

paper · pdf · doi:10.48550/arxiv.2002.04336

arxiv created 2020/09/25 · arxiv updated 2020/09/29

Abstract

We aim to reconstruct a monoid scheme X from the category of quasi-coherent sheaves over it. This is much in the vein of Gabriel's original reconstruction theorem. Under some finiteness condition on a monoid schemes X, we show that the localising subcategories of the topos \mathfrakQc(X) of quasi-coherent sheaves on X is in a one-to-one correspondence with open subsets of X, while the elements of X correspond to the topos points of \mathfrakQc(X). This allows us to reconstruct X from \mathfrakQc(X).

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