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arXiv · 1703.06479

Lift of Frobenius and Descent to Constants

Arnab Saha
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Abstract

In differential algebra, a proper scheme $X$ defined over an algebraically closed field $K$ with a derivation $\partial$ on it descends to the field of constants $K^\partial$ if $X$ itself lifts the derivation $\partial$. This is a result by A. Buium. Now in the arithmetic case, the notion of a derivation is replaced by the notion of a $π$-derivation $δ$ or equivalently in the flat case, a lift of Frobenius $ϕ$. We will show an analogous result in the arithmetic case of equal characteristic. We show our results using the arithmetic analogue of Taylor expansion using Witt vectors.

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Arnab Saha. 2017-04-19. Lift of Frobenius and Descent to Constants. https://arxiv.org/abs/1703.06479

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