Geometricity of the Hodge filtration on the $\infty$-stack of perfect complexes over $X_{DR}$
| dc.creator | Simpson, Carlos T. | |
| dc.date | 2005-10-13 | |
| dc.date | 2008-04-29 | |
| dc.date.accessioned | 2026-07-07T09:35:40Z | |
| dc.date.available | 2026-07-07T09:35:40Z | |
| dc.description | We construct a locally geometric $\infty$-stack $M_{Hod}(X,Perf)$ of perfect complexes with $λ$-connection structure on a smooth projective variety $X$. This maps to $A ^1 / G_m$, so it can be considered as the Hodge filtration of its fiber over 1 which is $M_{DR}(X,Perf)$, parametrizing complexes of $D_X$-modules which are $O_X$-perfect. We apply the result of Toen-Vaquie that $Perf(X)$ is locally geometric. The proof of geometricity of the map $M_{Hod}(X,Perf) \to Perf(X)$ uses a Hochschild-like notion of weak complexes of modules over a sheaf of rings of differential operators. We prove a strictification result for these weak complexes, and also a strictification result for complexes of sheaves of $O$-modules over the big crystalline site. | |
| dc.identifier | https://arxiv.org/abs/math/0510269 | |
| dc.identifier | http://arxiv.org/abs/math/0510269 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159906 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Geometricity of the Hodge filtration on the $\infty$-stack of perfect complexes over $X_{DR}$ | |
| dc.type | text |