Timeline for Exponentials in the opposite category of finite separable algebras
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 20, 2013 at 6:24 | vote | accept | Fujita Tomomi | ||
| Nov 20, 2013 at 1:29 | history | edited | Marguax | CC BY-SA 3.0 |
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| Nov 19, 2013 at 23:31 | comment | added | Fujita Tomomi | Oh, I didn't know its motivations. Thanks a lot! | |
| Nov 19, 2013 at 23:05 | comment | added | Marguax | @Fujita: It is curious that you know a bit about algebraic spaces but not Hom-schemes, as Grothendieck's work on Hilbert schemes, Hom-schemes, Picard schemes etc. predates Artin's work on algebraic spaces and provides much of the motivation for it. I highly recommend the chapter on Hilbert schemes in the book "FGA Explained" (which should discuss Hom-schemes as an application). But for finite flat schemes over a locally noetherian base, Hom-schemes can be built by bare hands as affine over the base: just chase structure constants for algebra structure on vector bundles (good exercise). Enjoy. | |
| Nov 19, 2013 at 23:01 | history | edited | Marguax | CC BY-SA 3.0 |
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| Nov 19, 2013 at 22:56 | comment | added | Marguax | @Fujita: sorry, I was getting the algebra and geometry mixed up; you are right that it is an $n$-fold tensor product, or more naturally a tensor power indexed by $I$. I will fix this. | |
| Nov 19, 2013 at 22:36 | comment | added | Fujita Tomomi | However, is your answer for the case $B=K^n$ right? I suppose in this case, $C^B$ is seemed to be just a n-times tensor $C \otimes C \otimes \dots \otimes C$. | |
| Nov 19, 2013 at 21:59 | comment | added | Fujita Tomomi | Thank you very much! Although I did know a little about algebraic spaces, I didn't know the notion of Hom-Schemes at all and these very interesting connection. Do you know some textbooks which include these interesting matters? | |
| Nov 19, 2013 at 20:29 | history | edited | Marguax | CC BY-SA 3.0 |
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| Nov 19, 2013 at 16:22 | history | answered | Marguax | CC BY-SA 3.0 |