Endomorphism rings of formal 𝐴₀-modules

Yamagata, Shuji

doi:10.1090/S0002-9947-1990-0967319-5

Endomorphism rings of formal $A_ 0$-modules
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by Shuji Yamagata PDF

Trans. Amer. Math. Soc. 320 (1990), 615-623 Request permission

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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