The action of the Frobenius map on rank 2 vector bundles over genus 2 curves in small characteristics
| dc.creator | Ducrohet, Laurent | |
| dc.date | 2005-12-27 | |
| dc.date.accessioned | 2026-07-07T06:55:48Z | |
| dc.date.available | 2026-07-07T06:55:48Z | |
| dc.description | Let $X$ be genus 2 curve defined over an algebraically closed field of characteristic $p$ and let $X\_1$ be its $p$-twist. Let $M\_X$ (resp. $M\_{X\_1}$) be the (coarse) moduli space of semi-stable rank 2 vector bundles with trivial determinant over $X$ (resp. $X\_1$). The moduli space $M\_X$ is isomorphic to the 3-dimensional projective space and is endowed with an action of the group $J[2]$ of order 2 line bundles over $X$. When $3\leq p \leq 7$, we show that the Verschiebung (i.e., the separable part of the action of Frobenius by pull-back) $V : M\_{X\_1} \dashrightarrow M\_X$ is completely determined by its restrictions to the lines that are invariant under the action of a non zero element of $J[2]$. Those lines correspond to elliptic curves that appear as Prym varieties and the Verschiebung restricts to the morphism induced by multiplication by $p$. Therefore, we are able to compute the explicit equations of the Verschiebung when the base field has characteristic 3, 5 or 7. | |
| dc.identifier | https://arxiv.org/abs/math/0512597 | |
| dc.identifier | http://arxiv.org/abs/math/0512597 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106402 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60 | |
| dc.title | The action of the Frobenius map on rank 2 vector bundles over genus 2 curves in small characteristics | |
| dc.type | text |