Density of vector bundles periodic under the action of Frobenius

作者：Ducrohet Laurent^*; Mehta Vikram B

来源：Bulletin des Sciences Mathematiques, 2010, 134(5): 454-460.

DOI：10.1016/j.bulsci.2009.11.001

• Vector bundles
• Frobenius action
• Difference geometry
• Fundamental group

Let X be a proper and smooth curve of genus g >= 2 over an algebraically closed field k of positive characteristic. If k = (F) over bar (p), 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.

• 出版日期2010-8