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 Mapc(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 Gn, this profinite group is the semi-direct product of the Morava stabilizer group Sn with the Galois group of the field extension Fpn/ Fp.
The objects K(n)–the n-th Morava K-theory spectrum, En–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 E2-term of the K( n)-local En-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*( LK(n)( En ∧
The term Hs(lim1 i≥0Mapc(G*n, π t+1(Xi))) 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|
|School Location:||United States -- Louisiana|
|Source:||DAI-B 79/09(E), Dissertation Abstracts International|
|Keywords:||Continuous cohomology, E2-term, K(n)-local En-Adams, Milnor short exact sequence, Spectral sequence|
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