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- W2568124549 abstract "For any ring $R$ let $Lambda (R)$ denote the multiplicative group of power series of the form $1 + {a_1}t + cdots$ with coefficients in $R$. The Artin-Hasse exponential mappings are homomorphisms $W_{p, infty } (k) to Lambda ({W_{p, infty }}(k))$, which satisfy certain additional properties. Somewhat reformulated, the Artin-Hasse exponentials turn out to be special cases of a functorial ring homomorphism $E: {W_{p, infty }}( - ) to {W_{p,infty }}({W_{p,infty }}( - ))$, where ${W_{p,infty }}$ is the functor of infinite-length Witt vectors associated to the prime $p$. In this paper we present ramified versions of both ${W_{p,infty }}( - )$ and $E$, with ${W_{p,infty }}( - )$ replaced by a functor $W_{q,infty }^F( - )$, which is essentially the functor of $q$-typical curves in a (twisted) Lubin-Tate formal group law over $A$, where $A$ is a discrete valuation ring that admits a Frobenius-like endomorphism $sigma$ (we require $sigma (a) equiv {a^q} bmod mathfrak {m}$ for all $a in A$, where $mathfrak {m}$ is the maximal idea of $A$). These ramified-Witt-vector functors $W_{q,infty }^F( - )$ do indeed have the property that, if $k = A/mathfrak {m}$ is perfect, $A$ is complete, and $l/k$ is a finite extension of $k$, then $W_{q,infty }^F(l)$ is the ring of integers of the unique unramified extension $L/K$ covering $l/k$." @default.
- W2568124549 created "2017-01-13" @default.
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- W2568124549 date "1980-05-01" @default.
- W2568124549 modified "2023-09-25" @default.
- W2568124549 title "Twisted Lubin-Tate Formal Group Laws, Ramified Witt Vectors and (Ramified) Artin-Hasse Exponentials" @default.
- W2568124549 doi "https://doi.org/10.2307/1998143" @default.
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