Reconstruction theorem for monoid schemes

[摘要] 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 Q(c)(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 Q(c)(X). This allows us to reconstruct X from Q(c)(X). (c) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-01

[关键词] Commutative monoid;Monoid scheme;Topos;Localisations of categories;Topos points