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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Endomorphism rings of formal $ A\sb 0$-modules


Author: Shuji Yamagata
Journal: Trans. Amer. Math. Soc. 320 (1990), 615-623
MSC: Primary 14L05; Secondary 11S31
MathSciNet review: 967319
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Abstract: Let $ {A_0}$ be the valuation ring of a finite extension $ {K_0}$ of $ {Q_p}$ and $ A \supset {A_0}$ be a complete discrete valuation ring with the perfect residue field. We consider the endomorphism rings of $ n$-dimensional formal $ {A_0}$-modules $ \Gamma $ over $ A$ of finite $ {A_0}$-height with reduction absolutely simple up to isogeny. Especially we prove commutativity of $ {\operatorname{End} _{A,{A_0}}}(\Gamma )$. Given an arbitrary finite unramified extension $ {K_1}$ of $ {K_0}$, a variety of examples (different dimensions and different $ {A_0}$-heights) is constructed whose absolute endomorphism rings are isomorphic to the valuation ring of $ {K_1}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0967319-5
PII: S 0002-9947(1990)0967319-5
Keywords: Formal modules (groups), endomorphism rings
Article copyright: © Copyright 1990 American Mathematical Society