Abstract
Let G be a p-divisible formal group law over an algebraically closed field of characteristic p. We show that certain equivariant vector bundles on the universal deformation space of G give rise to pseudocompact modules over the Iwasawa algebra of the automorphism group of G. Passing to global rigid analytic sections, we obtain representations which are topologically dual to locally analytic representations. In studying these, one is led to the consideration of divided power completions of universal enveloping algebras. The latter seem to constitute a novel tool in p-adic representation theory.
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Notes
- 1.
Here \(\varphi _{{\ast}}(\mathbb{G},\rho _{\mathbb{G}}) = (\varphi _{{\ast}}(\mathbb{G}),\rho _{\mathbb{G}})\) , where \(\varphi _{{\ast}}\mathbb{G}\) is obtained by applying \(\varphi\) to the coefficients of \(\mathbb{G}\) . Since \(\varphi\) induces an isomorphism between the residue class fields of \(R_{G}^{\mathop{\text{def}}\nolimits }\) and R, we may identify \(\mathbb{G}\,\mathrm{mod}\,\mathfrak{m}_{ R_{G}^{\mathop{\text{def}}\nolimits }}\) and \(\varphi _{{\ast}}\mathbb{G}\,\mathrm{mod}\,\mathfrak{m}\).
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Kohlhaase, J. (2014). Iwasawa Modules Arising from Deformation Spaces of p-Divisible Formal Group Laws. In: Bouganis, T., Venjakob, O. (eds) Iwasawa Theory 2012. Contributions in Mathematical and Computational Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55245-8_10
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