Relative Zariski Open Objects
| dc.creator | Marty, Florian | |
| dc.date | 2007-12-21 | |
| dc.date | 2009-05-12 | |
| dc.date.accessioned | 2026-07-07T13:13:15Z | |
| dc.date.available | 2026-07-07T13:13:15Z | |
| dc.description | In [TV], Bertrand Toën and Michel Vaquié define a scheme theory for a closed monoidal category $(\mathcal{C},\otimes,1)$. One of the key ingredients of this theory is the definition of a Zariski topology on the category of commutative monoids in $\mathcal{C}$. The purpose of this article is to prove that under some hypotheses, Zariski open subobjects of affine schemes can be classified almost as in the usual case of rings $(Z-mod,\otimes,Z)$. The main result states that for any commutative monoid $A$, the locale of Zariski open subobjects of the affine scheme $Spec(A)$ is associated to a topological space whose points are prime ideals of $A$ and open subsets are defined by the same formula as in rings. As a consequence, we compare the notions of scheme over $\mathbb{F}_{1}$ of [D] and [TV]. | |
| dc.description | 19 pages. A more general main theorem has been proved. The organisation has been modified | |
| dc.identifier | https://arxiv.org/abs/0712.3676 | |
| dc.identifier | http://arxiv.org/abs/0712.3676 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229830 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Category Theory | |
| dc.title | Relative Zariski Open Objects | |
| dc.type | text |