Timeline for Pushouts in the Category of Schemes
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Feb 14, 2021 at 23:57 | history | suggested | HDB | CC BY-SA 4.0 |
improved formatting
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| Feb 14, 2021 at 22:10 | review | Suggested edits | |||
| S Feb 14, 2021 at 23:57 | |||||
| Nov 12, 2011 at 13:59 | comment | added | Qfwfq | @Martin: yes, my answer was only meant to be a (very) partial answer. | |
| Nov 12, 2011 at 11:22 | comment | added | Martin Brandenburg | @Qfwfg: Your pushout is really only the pushout in the category of affine schemes. For non-affine schemes, in general, your pushout does noes have the desired universal property. One has to require, for example, that $\phi$ or $\psi$ is surjective (see the paper by Karl Schwede). | |
| Apr 17, 2010 at 7:16 | comment | added | Harry Gindi | I fixed it for you. | |
| Apr 17, 2010 at 7:16 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 41 characters in body
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| Apr 17, 2010 at 6:36 | comment | added | Qfwfq | I think I meant something like the "fibered coproduct of schemes". That is, the opposite notion to the actual fibered product in CRings (and the latter corresponds, if I'm not mistaken, to my definition of $D$). | |
| Apr 17, 2010 at 5:52 | comment | added | Harry Gindi | The coproduct in CRing is given by the tensor product over $\mathbb{Z}$, and the pushout over $R$ is given by the tensor product over $R$. I suspect you meant the pullback of A and B over R, written $A\times_R B$. Also, the "coproduct" that you're referring to is called the pushout, the gluing, or the "fibered coproduct", although this last one is nonstandard. The coproduct of affine schemes is specifically the disjoint union. | |
| Apr 17, 2010 at 5:02 | history | answered | Qfwfq | CC BY-SA 2.5 |