On Deep Frobenius Descent and Flat Bundles
نویسنده
چکیده
Let R be an integral domain of finite type over Z and let f : X → SpecR be a smooth projective morphism of relative dimension d ≥ 1. We investigate, for a vector bundle E on the total space X , under what arithmetical properties of a sequence (pn, en)n∈N, consisting of closed points pn in SpecR and Frobenius descent data Epn ∼= F n(F) on the closed fibers Xpn , the bundle E0 on the generic fiber X0 is semistable. Mathematical Subject Classification (2000): 14H60.
منابع مشابه
A Remark on Frobenius Descent for Vector Bundles
We give a class of examples of a vector bundle on a relative smooth projective curve over SpecZ such that for infinitely many prime reductions the bundle has a Frobenius descent, but the generic restriction in characteristic zero is not semistable. Mathematical Subject Classification (2000): primary: 14H60, secondary: 13A35.
متن کاملFiber bundles and Lie algebras of top spaces
In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.
متن کاملSlope filtrations for relative Frobenius
The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over the Robba ring (the ring of germs of rigid analytic functions on an unspecified open annulus of outer radius 1) over a discretely valued field. In this paper, we give a third-generation proof of this theorem, which...
متن کاملOn vector bundles destabilized by Frobenius pull-back
Let X be a smooth projective curve of genus g > 1 over an algebraically closed field of positive characteristic. This paper is a study of a natural stratification, defined by the absolute Frobenius morphism of X, on the moduli space of vector bundles. In characteristic two, there is a complete classification of semi-stable bundles of rank 2 which are destabilized by Frobenius pull-back. We also...
متن کاملThe Frobenius map , rank 2 vector bundles and Kummer ’ s quartic surface in characteristic 2 and 3 Yves Laszlo and Christian Pauly
Our interest in the diagram (1.1) comes from questions related to the action of the Frobenius map on vector bundles like e.g. surjectivity of V , density of Frobenius-stable bundles, loci of Frobenius-destabilized bundles (see [LP]). These questions are largely open when the rank of the bundles, the genus of the curve or the characteristic of the field are arbitrary. In [LP] we made use of the ...
متن کامل