Mathematics – Algebraic Geometry
Scientific paper
2007-12-21
Mathematics
Algebraic Geometry
19 pages. A more general main theorem has been proved. The organisation has been modified
Scientific paper
In [TV], Bertrand To\"en and Michel Vaqui\'e 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].
No associations
LandOfFree
Relative Zariski Open Objects does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Relative Zariski Open Objects, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Relative Zariski Open Objects will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-696665