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Lubin-Tate Deformation Spaces and $(phi,Gamma)$-Modules | | Annie Carter
; | | Date: |
2 May 2016 | | Abstract: | Jean-Marc Fontaine has shown that there exists an equivalence of categories
between the category of continuous $mathbb{Z}_p$-representations of a given
Galois group and the category of ’{e}tale $(phi,Gamma)$-modules over a
certain ring. This work attempts to answer the question of whether there exists
a theory of $(phi,Gamma)$-modules for the Lubin-Tate tower. We construct this
tower via the rings $R_n$ which parametrize deformations of level $n$ of a
given formal module. One can choose prime elements $pi_n$ in each ring $R_n$
in a compatible way, and consider the tower of fields $(K’_n)_n$ obtained by
localizing at $pi_n$, completing, and passing to fraction fields. By taking
the compositum $K_n = K_0 K’_n$ of each field with a certain unramified
extension $K_0$ of the base field $K’_0$ one obtains a tower of fields
$(K_n)_n$ which is strictly deeply ramified in the sense of Anthony Scholl.
This is a first step towards showing that there exists a theory of
$(phi,Gamma)$-modules for this tower. | | Source: | arXiv, 1605.0615 | | Services: | Forum | Review | PDF | Favorites | |
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