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arXiv · 1703.07010

On Frobenius and Fibers of Arithmetic Jet Spaces

James Borger·Arnab Saha
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Abstract

In this article, given a scheme $X$ we show the existence of canonical lifts of Frobenius maps in an inverse system of schemes obtained from the fiber product of the canonical prolongation sequence of arithmetic jet spaces $J^*X$ and a prolongation sequence $S^*$ over the scheme $X$. As a consequence, for any smooth group scheme $E$, if $N^n$ denote the kernel of the canonical projection map of the $n$-th jet space $J^nE \rightarrow E$, then the inverse system $\{N^n\}_n$ is a prolongation sequence.

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James Borger, Arnab Saha. 2017-03-21. On Frobenius and Fibers of Arithmetic Jet Spaces. https://arxiv.org/abs/1703.07010

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