Cusps and $\D$-Modules
| dc.creator | Ben-Zvi, David | |
| dc.creator | Nevins, Thomas | |
| dc.date | 2002-12-05 | |
| dc.date | 2003-10-09 | |
| dc.date.accessioned | 2026-07-07T04:53:35Z | |
| dc.date.available | 2026-07-07T04:53:35Z | |
| dc.description | We study interactions between the categories of $\D$-modules on smooth and singular varieties. For a large class of singular varieties $Y$, we use an extension of the Grothendieck--Sato formula to show that $\D_Y$-modules are equivalent to stratifications on $Y$, and as a consequence are unaffected by a class of homeomorphisms, the {\em cuspidal quotients}. In particular, when $Y$ has a smooth bijective normalization $X$, we obtain a Morita equivalence of $\D_Y$ and $\D_X$ and a Kashiwara theorem for $\D_Y$, thereby solving conjectures of Hart-Smith and Berest-Etingof-Ginzburg (generalizing results for complex curves and surfaces and rational Cherednik algebras). We also use this equivalence to enlarge the category of induced $\D$-modules on a smooth variety $X$ by collecting induced $\D_X$-modules on varying cuspidal quotients. The resulting {\em cusp-induced} $\D_X$-modules possess both the good properties of induced $\D$-modules (in particular, a Riemann-Hilbert description) and, when $X$ is a curve, a simple characterization as the generically torsion-free $\D_X$-modules. | |
| dc.description | Final version, to appear in J. Amer. Math. Soc. (2004) | |
| dc.identifier | https://arxiv.org/abs/math/0212094 | |
| dc.identifier | http://arxiv.org/abs/math/0212094 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65907 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.title | Cusps and $\D$-Modules | |
| dc.type | text |