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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Galois endomorphisms of the torsion subgroup of one-parameter generic formal groups


Author: Karl Zimmermann
Journal: Proc. Amer. Math. Soc. 102 (1988), 22-24
MSC: Primary 14L05,; Secondary 11G07,11S31
MathSciNet review: 915708
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0915708-3
PII: S 0002-9939(1988)0915708-3
Keywords: One parameter formal group, local ring
Article copyright: © Copyright 1988 American Mathematical Society