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Two ways to compute Galois Cohomology using Lubin-Tate (φ, Γ)-modules, a Reciprocity Law and a Regulator Map

Kupferer, Benjamin Josef

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The main focus of the present thesis lays on general Lubin-Tate (φ,Γ)-modules. Before heading towards this theory, we discuss some general facts about monoid and continuous group cohomology as well as double complexes and limits of complexes. After these preliminaries we first show as in the classical case that the category of étale (φ,Γ)-modules is equivalent to the category of Galois representations of the absolute Galois group of K with coefficients in O_L, where K|L and L|Q_p are finite extensions. Using (φ, Γ)-modules, we then compute Iwasawa cohomology of such a representation and define a reciprocity map. Afterwards we compute the Galois cohomology groups using (φ, Γ)-modules. To do this, we construct two complexes of (φ, Γ)-modules whose cohomologies each coincide with the cohomology of the attached Galois representation. One of these two complexes is constructed by using the operator φ the other one by using the operator ψ. Finally, we construct a regulator map for an O_L × Z_p-extension of L.

Item Type: Dissertation
Supervisor: Venjakob, Prof. Dr. Otmar
Place of Publication: Heidelberg
Date of thesis defense: 29 May 2020
Date Deposited: 05 Jun 2020 13:36
Date: 2020
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Algebraische Zahlentheorie
Uncontrolled Keywords: (φ,Γ)-Moduln
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