Reconstruction theorem for monoid schemes

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 localisations of the topos Qc ( X ) of quasi-coherent sheaves on X are in a one-to-one correspondence with open subsets of X , while the elements of X correspond to the topos points of Qc ( X ) . This allows us to reconstruct X from Qc ( X ) .