Density of vector bundles periodic under the action of Frobenius

Ducrohet, Laurent ; Mehta, V. B. (2010) Density of vector bundles periodic under the action of Frobenius Bulletin des Sciences Mathématiques, 134 (5). pp. 454-460. ISSN 0007-4497

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00074...

Related URL: http://dx.doi.org/10.1016/j.bulsci.2009.11.001

Abstract

Let X be a proper and smooth curve of genus g≥2 over an algebraically closed field k of positive characteristic. If k=Fp, it follows from Hrushovski's work on the geometry of difference schemes that the set of rank r vector bundles with trivial determinant over X that are periodic under the action of Frobenius is dense in the corresponding moduli space. Using the equivalence between Frobenius periodicity of a stable vector bundle and its triviality after pull-back by some finite etale cover of X (due to Lange and Stuhler) on the one hand, and specialization of the fundamental group on the other hand, we prove that the same result holds for any algebraically closed field of positive characteristic.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Vector Bundles; Frobenius Action; Difference Geometry; Fundamental Group
ID Code:20425
Deposited On:20 Nov 2010 14:31
Last Modified:06 Jun 2011 11:07

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