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On the Iwasawa theory of the Lubin–Tate moduli space
- Part of
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- Journal:
- Compositio Mathematica / Volume 149 / Issue 5 / May 2013
- Published online by Cambridge University Press:
- 26 February 2013, pp. 793-839
- Print publication:
- May 2013
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- Article
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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 
$R$.
