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Let n ≥ 1 be any integer and let p be a prime number. For a profinite group G and any discrete abelian group M, we use Map^{c}(G, M ) to denote the abelian group of continuous functions from G to M. For the most part, our interests lie in a particular profinite group known as the extended Morava stabilizer group. Denoted by G_{n}, this profinite group is the semi-direct product of the Morava stabilizer group Sn with the Galois group of the field extension F_{pn}/ F_{p}.
The objects K(n)–the n-th Morava K-theory spectrum, E_{n}–the Lubin-Tate spectrum, and E(n)–the Johnson-Wilson spectrum, are essential to this dissertation. By using the setting of symmetric spectra, we provide a cohomological approximation of the E_{2}-term of the K( n)-local E_{n}-Adams spectral sequence. Given any spectrum X, LK( n)(X) denotes the Bousfield localization of X with respect to K(n), while E_{ *}^{∨}(X) denotes π_{*}( L_{K}(_{n})( E_{n} ∧
The term H^{s}(lim^{1}_{ i≥0}Map^{c}(G^{*}_{n}, π_{ t+1}(X_{i}))) plays a vital role in this dissertation, and in an attempt to simplify it, we provide an analysis of the relationship between the first derived functor of the inverse limit of non-negatively-graded towers of abelian groups and the functor Map^{ c}(G, –).
Advisor: | Davis, Daniel G. |
Commitee: | Gonzalez, Leonel R., Magidin, Arturo, Rogers, Christopher |
School: | University of Louisiana at Lafayette |
Department: | Sciences |
School Location: | United States -- Louisiana |
Source: | DAI-B 79/09(E), Dissertation Abstracts International |
Source Type: | DISSERTATION |
Subjects: | Mathematics |
Keywords: | Continuous cohomology, E2-term, K(n)-local En-Adams, Milnor short exact sequence, Spectral sequence |
Publication Number: | 10623147 |
ISBN: | 9780355854077 |