D-modules on affine space that are regular at infinity - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T04:11:11Z http://mathoverflow.net/feeds/question/65478 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65478/d-modules-on-affine-space-that-are-regular-at-infinity D-modules on affine space that are regular at infinity Ben Webster 2011-05-19T22:05:30Z 2011-05-19T22:51:32Z <p>If I have a D-module $M$ on $\mathbb{A}^n$ (which is essentially the same thing as a module over the Weyl algebra), then I can push this D-module forward to $\mathbb{P}^n$ to get a D-module $j_*M$ on the projective closure.</p> <blockquote> <p>Is there an intrinsic description of those $M$ such that $j_*M$ are regular on the divisor at $\infty$?</p> </blockquote> http://mathoverflow.net/questions/65478/d-modules-on-affine-space-that-are-regular-at-infinity/65481#65481 Answer by YBL for D-modules on affine space that are regular at infinity YBL 2011-05-19T22:51:32Z 2011-05-19T22:51:32Z <p>In dimension one, $j_*M$ is regular at infinity iff the Fourier transform $F(M)$ has no singularity outside 0 and $\infty$. The reason is obviously that Fourier exchanges the D-modules $\delta_c = D/D(t-c)$ et $Oe^{ct} = D/D(\partial_t-c)$. There's probably a generalization for higher dimensions but I've never seen it. </p>