Direct images of bundles under Frobenius morphisms
| dc.creator | Sun, Xiaotao | |
| dc.date | 2006-11-13 | |
| dc.date | 2008-03-31 | |
| dc.date.accessioned | 2026-07-07T09:29:13Z | |
| dc.date.available | 2026-07-07T09:29:13Z | |
| dc.description | Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. For any vector bundle $W$ on $X$, we prove that instability of $F_*W$ is bounded by instability of $W\otimes{\rm T}^{\ell}(Ω^1_X)$ ($0\le \ell\le n(p-1)$)(Corollary \ref{cor3.8}). When $X$ is a smooth projective curve of genus $g\ge 2$, it implies $F_*W$ being stable whenever $W$ is stable. | |
| dc.description | the final version to appear in Invent. math. (2008) | |
| dc.identifier | https://arxiv.org/abs/math/0611360 | |
| dc.identifier | http://arxiv.org/abs/math/0611360 | |
| dc.identifier | doi:10.1007/s00222-008-0125-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157704 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60, 14D20, 13A35 | |
| dc.title | Direct images of bundles under Frobenius morphisms | |
| dc.type | text |