Representability of $GL_E$
| dc.creator | Nitsure, Nitin | |
| dc.date | 2002-04-03 | |
| dc.date | 2002-11-27 | |
| dc.date.accessioned | 2026-07-07T04:47:26Z | |
| dc.date.available | 2026-07-07T04:47:26Z | |
| dc.description | Let $S$ be a noetherian scheme, and let $E$ be a coherent sheaf on it. We define a group-valued contravariant functor $GL_E$ on $S$-schemes by associating to any $S$-scheme $T$ the group $GL_E(T)$ of all linear automorphisms of the pullback of $E$ to $T$. This functor is clearly a sheaf in the fpqc topology. We prove that $GL_E$ is representable by a group-scheme over $S$ if and only if the sheaf $E$ is locally free. | |
| dc.description | 3 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0204047 | |
| dc.identifier | http://arxiv.org/abs/math/0204047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63711 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14L15 | |
| dc.title | Representability of $GL_E$ | |
| dc.type | text |