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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 $R$.

A conjecture is formulated which relates the equivariant local epsilon constant of a Galois extension of $p$-adic fields to a natural algebraic invariant coming from étale cohomology. Some evidence for the conjecture is provided and its relation to a conjecture for the equivariant global epsilon constant of an extension of number fields formulated by Bley and Burns is established.

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On the Iwasawa theory of the Lubin–Tate moduli space

EQUIVARIANT LOCAL EPSILON CONSTANTS AND ÉTALE COHOMOLOGY

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On the Iwasawa theory of the Lubin–Tate moduli space

EQUIVARIANT LOCAL EPSILON CONSTANTS AND ÉTALE COHOMOLOGY