Abstract

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Quillen proved in 1969 that every endomorphism of a simple module over the 

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universal enveloping algebra of a finite dimensional Lie algebra is algebraic 

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over the ground field. Affinoid enveloping algebras are certain p-adic 

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completions enveloping algebras and arise as particular microlocalisations of 

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Iwasawa algebras. I wlll explain how to prove an exact analogue of Quillen's 

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result for simple modules over these affinoid enveloping algebras. This is 

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joint work with Simon Wadsley.