On deep Frobenius descent and flat bundles
Abstract
Let R be an integral domain of finite type over Z and let f:X --> Spec R 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 ∈ , consisting of closed points pn in Spec R and Frobenius descent data Epn Fen*(F) on the closed fibers Xpn, the bundle E0 on the generic fiber X0 is semistable.
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