Timeline for Does regularity of a D-module for an unusual filtration imply regularity for the usual one?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Sep 20, 2011 at 23:23 | comment | added | Alexander Braverman | Do you mean that the $D$-module is regular on ${\mathbb A}^n$ without infinity? In this case I would be interested to see the proof of your original statement. In any case if you take your $D$-module to be $exp(1/x)$ on ${\mathbb A}^1$ and set $deg(x)=-1$ and $deg(d)=2$ then you can define a filtration $M_i$ to be generated over functions by all $p(x)exp(1/x)$ where $p(x)$ is a polynomial in $x^{-1}$ of degree $\leq i$ and I think it gives a counterexample. | |
| Sep 20, 2011 at 22:49 | comment | added | Alexander Braverman | Ben, I am confused about your definition of regularity. If you take the D-module generated by $e^x$ on ${\mathbb A}^1$ it obviously has a filtration such that the associated graded is the structure sheaf of the zero section in the cotangent bundle and it is not regular. What am I missing? | |
| Sep 19, 2011 at 22:22 | history | asked | Ben Webster♦ | CC BY-SA 3.0 |