Timeline for D-module that is coherent as O-module
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2013 at 3:31 | vote | accept | Serge Lvovski | ||
| Jan 10, 2013 at 22:16 | history | edited | inkspot | CC BY-SA 3.0 |
Errors corrected and a query answered
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| Jan 10, 2013 at 19:04 | comment | added | David Ben-Zvi | Also projectivity should not be necessary, the argument you give (and construction of flattening stratification) is local.. maybe Noetherian?? | |
| Jan 10, 2013 at 19:04 | comment | added | David Ben-Zvi | Note that in characteristic p the statement is false even for X smooth if by $D_X$ you mean the ring of "crystalline diffops" (generated by functions and vector fields), rather than the full divided power ring (whose modules are the same as stratifications) -- eg Frobenius pullback of any coherent sheaf is a D-module. | |
| Jan 10, 2013 at 18:43 | comment | added | Serge Lvovski |
I am sorry, could you, please, explain in more detail how you conclude that for every $i$ there is a $j$ such that $p_1^{-1}(X_i)=p_2^{-1}(X_j)$?
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| Jan 10, 2013 at 18:21 | comment | added | David Ben-Zvi | This is a very nice argument, but is it clear it applies to D-modules? your definition is that of a stratification (or comodule over jets), which I don't think are the same as modules over the ring of differential operators in general (yours is the much better behaved one in general). I only know they are the same for varieties with only cusp singularities, for which all the various notions of D-module coincide. | |
| Jan 10, 2013 at 18:07 | history | answered | inkspot | CC BY-SA 3.0 |