On the Iwasawa theory of the Lubin–Tate moduli space

We study the affine formal algebra$R$of the Lubin–Tate deformation space as a module over two different rings. One is the completed group ring of the automorphism group$\Gamma $of the formal module of the deformation problem, the other one is the spherical Hecke algebra of a general linear group. In the most basic case of height two and ground field$\mathbb {Q}_p$, our structure results include a flatness assertion for$R$over the spherical Hecke algebra and allow us to compute the continuous (co)homology of$\Gamma $with coefficients in $R$.