Frobenius pull backs of vector bundles in higher dimensions

Details Frobenius pull backs of vector bundles in higher dimensions Frobenius pull backs of vector bundles in higher dimensions

2010-11-09

arxiv.org/abs/1011.1971v2

Mathematics

Algebraic Geometry

13 pages. This is a revised version of the paper 1011.1971 in math.AG

Scientific paper

Here we prove that for a smooth projective variety $X$ of arbitrary dimension and for a vector bundle $E$ over $X$, the Harder-Narasimhan filtration of a Frobenius pull back of $E$ is a refinement of the Frobenius pull-back of the Harder-Narasimhan filtration of $E$, provided there is a lower bound on the characteristic $p$ (in terms of rank of $E$ and the slope of the destabilising sheaf of the cotangent bundle of $X$). We also recall some examples, due to Raynaud and Monsky,to show that some lower bound on $p$ is necessary. We further prove an analogue of this result for principal $G$-bundles over $X$. We also give a bound on the instability degree of the Frobenius pull back of $E$ in terms of the instability degree of $E$ and well defined invariants ot $X$ and $E$.

Affiliated with

Also associated with

No associations

Rating

Frobenius pull backs of vector bundles in higher dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Frobenius pull backs of vector bundles in higher dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Frobenius pull backs of vector bundles in higher dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-492615