Timeline for What is the standard reference on "infinitesimal space" in algebraic geometry??
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| Jan 27, 2010 at 15:37 | answer | added | Marty | timeline score: 5 | |
| Jan 21, 2010 at 21:34 | comment | added | Lars | If I understand your question correctly, for the commutative case you should have a look at EGA IV, §16 and any book discussing formal completion along subschemes, say Hartshorne or EGA I. As for the connection of D-Modules and Crystals, the already mentioned book of Berthelot-Ogus is very nice. Then there is also Berthelot's LNM Text on Crystalline Cohomology. I also really enjoyed these notes: math.harvard.edu/~gaitsgde/grad%5F2009/SeminarNotes/… | |
| Jan 20, 2010 at 0:45 | comment | added | Clark Barwick | I'm afraid I don't understand what topic you're seeking a reference in. What sort of "spaces" are you asking about? Vector spaces? Topological spaces? Schemes? Algebraic spaces? Sheaves on some site? What is the "serious issue" you're referring to? | |
| Jan 14, 2010 at 19:11 | comment | added | S. Carnahan♦ | It sounds like you're looking for references on commutative Artinian local rings, since their spectra are the "fat points" in algebraic geometry. Alternatively, you may want to look for references on deformation theory, since they use such structures a lot. Illusie's Complexe Cotangent et Deformations seems to be the standard reference, but Hartshorne also wrote a book relatively recently. | |
| Jan 14, 2010 at 12:18 | comment | added | Harry Gindi | Isn't the whole thing about noncommutative geometry that there is no presentation of a scheme as a topological space with a sheaf of rings, but only as a functor of points in the smooth grothendieck topology on the category of nonabelian affine schemes (which is the opposite category of an appropriate category of rings)? My point here is kinda that you might have some trouble finding any stuff at all in noncommutative geometry written in commutative AG language (i.e. not written as functors of points.) I may have misunderstood what you meant though. | |
| Jan 14, 2010 at 9:25 | comment | added | Kevin H. Lin | Maybe Berthelot-Ogus "Notes on Crystalline Cohomology"? | |
| Jan 14, 2010 at 9:15 | history | asked | Peter Lee | CC BY-SA 2.5 |