Galois endomorphisms of the torsion subgroup of one-parameter generic formal groups
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- by Karl Zimmermann PDF
- Proc. Amer. Math. Soc. 102 (1988), 22-24 Request permission
Abstract:
Let ${{\mathbf {Z}}_p}$ be the ring of $p$-adic integers and let $\Gamma$ be a one-parameter generic formal group of finite height $h$ defined over ${{\mathbf {Z}}_p}\left [ {\left [ {{t_1}, \ldots ,{t_{h - 1}}} \right ]} \right ] = A$. Let $K$ be the field of fractions of $A,G = \operatorname {Gal}\left ( {\bar K/K} \right )$ and $T\left ( \Gamma \right )$ the Tate module of $\Gamma$. The purpose of this paper is to give an elementary proof that the $\operatorname {map}\operatorname {End}_{A}\left ( \Gamma \right ) \to \operatorname {End}_{G}\left ( {T\left ( \Gamma \right )} \right )$ is a surjection.References
- Jonathan Lubin and John Tate, Formal moduli for one-parameter formal Lie groups, Bull. Soc. Math. France 94 (1966), 49–59. MR 238854
- Jonathan Lubin, Galois endomorphisms of the torsion subgroup of certain formal groups, Proc. Amer. Math. Soc. 20 (1969), 229–231. MR 232769, DOI 10.1090/S0002-9939-1969-0232769-6
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
- J. T. Tate, $p$-divisible groups, Proc. Conf. Local Fields (Driebergen, 1966) Springer, Berlin, 1967, pp. 158–183. MR 0231827
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 22-24
- MSC: Primary 14L05,; Secondary 11G07,11S31
- DOI: https://doi.org/10.1090/S0002-9939-1988-0915708-3
- MathSciNet review: 915708