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- W2949755005 abstract "For $C$ a complete algebraically closed extension of $mathbb{Q}_p$, we show that a one-dimensional $p$-divisible group $G/ mathcal{O}_C$ can be defined over a complete discretely valued subfield $L subset C$ with Hodge-Tate period ratios contained in $L$ if and only if $G$ has CM, if and only if the period ratios generate an extension of $mathbb{Q}_p$ of degree equal to the height of the connected part of $G$. This is a $p$-adic analog of a classical transcendence result of Schneider which states that for $tau$ in the complex upper half plane, $tau$ and $j(tau)$ are simultaneously algebraic over $mathbb{Q}$ if and only if $tau$ is contained in a quadratic extension of $mathbb{Q}$. We also briefly discuss a conjectural generalization to shtukas with one paw." @default.
- W2949755005 created "2019-06-27" @default.
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- W2949755005 date "2016-10-17" @default.
- W2949755005 modified "2023-09-27" @default.
- W2949755005 title "Transcendence of the Hodge-Tate filtration" @default.
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- W2949755005 hasPublicationYear "2016" @default.
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