On deep Frobenius descent and flat bundles

• Autores: Holger Brenner, Almar Kaid
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 5-6, 2008, págs. 1101-1115
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n6.a3
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• Resumen

  • Let $R$ be an integral domain of finite type over $\ZZ$ and let $f:\shX \ra \Spec R$ be a smooth projective morphism of relative dimension $d \geq 1$. We investigate, for a vector bundle $\shE$ on the total space $\shX$, under what arithmetical properties of a sequence $(\fop_n, e_n)_{n \in \NN}$, consisting of closed points $\fop_n$ in $\Spec R$ and Frobenius descent data $\shE_{\fop_n} \cong {F^{e_n}}^*(\shF)$ on the closed fibers $\shX_{\fop_n}$, the bundle $\shE_0$ on the generic fiber $\shX_0$ is semistable.